Post 13.1 aur 13.2 mein base 10 aur 100 ke paas square kiye. Aaj base 1000: 996², 1007², 988². Ek hi naya dhyaan: base 1000 mein 3 zero, to right part ko 3 boxes. Phir ek mix: kisi bhi square ko dekh kar kaise tay karein ki base method lagayein, Chapter 6 wali “5 pe khatam” trick, round number wala rule, ya seedha multiply.
⏱ Before Timer: Pehle Purane Method Se
Pehle seedha method, ek doosre number pe dekho: 997². 997² = 997 × 997. 997 to 1000 se 3 kam hai, to 997 ko 1000 baar lo, phir 3 baar subtract karo (Chapter 10 jaisi soch).
- 997 × 1000 = 997000 (peeche teen 0).
- 997 × 3 = 1000 × 3 − 3 × 3 = 3000 − 9 = 2991. (997 ko 3 baar lena = 1000 ko 3 baar lo, phir har baar ka 3 subtract karo: 3 baar 3, yaani 9.)
- Subtract karo: 997000 − 2991 = 994009. (Aasaan path: 997000 − 3000 = 994000. Par 2991 to 3000 se 9 kam hai, yaani 9 zyada subtract kar diye, to 9 waapas add karo: 994000 + 9 = 994009.) To 997² = 994009.
Ab isi method se 996² khud karo, timer ke saath (jawab abhi mat dekhna).
Ab phone ya watch mein stopwatch (time measure karne wali watch) chalu kijiye. Neeche wala sawaal isi upar wale seedhe method (1000 baar lo, phir subtract karo) se kijiye, copy-pencil ke saath. Chaho to school wala column method bhi laga sakte ho. Jaise hi jawab mil jaaye, stopwatch rok dijiye aur apna time likh lijiye.
Mera time: ______ second
Jawab dekho
996² = 996 × 996 = 992016
Abhi trick nahi dekhni! Post ke end mein After Timer mein yahi sawaal trick se karenge aur dono time ki compare karenge. 😊
— 📌 charumam.com
✅ Pehle Yeh Aata Hai
Chahiye: Post 13.1–13.2 ka square base method, 1000 se subtract karna (Post 3.2), aur bade numbers padhna (lakh). Sab neeche ke boxes mein. Naye word:
📖 Word jo is post mein aayenge
- Base 1000: 998, 1004 jaise number ka base. 1000 mein 3 zero → right 3 boxes.
- Teen boxes bharna: right 16 aaye to 016 likho; 9 aaye to 009.
- Lakh: 100000 (100 hazaar). 992016 = nau lakh baanve hazaar solah.
- Round number ka square: 30² = 900: digit ka square (9), phir zero double (2 zero).
- Kaunsi trick: number dekh kar chunna: base ke paas → base method; 5 pe khatam → Chapter 6; round → zero rule; baaki → seedha.
📏 Bade numbers padhna aur round number mein add karna
Har digit ki ek jagah (place) hoti hai. Right se count karo: pehli jagah Ikai (ones, 1 wale), uske left mein Dahai (tens, 10 wale), phir Saikda (hundreds, 100 wale), phir Hazaar (thousands, 1000 wale).
10 ka bundle: 10 ikai = 1 dahai (10). 10 dahai = 1 saikda (100). 10 saikde = 1 hazaar (1000). Har jagah apne right wali jagah se 10 times badi hai.
| Number | Kaise padhein | Kis cheez se bana |
|---|---|---|
| 98 | attaanve | 9 dahai (90) + 8 ikai |
| 165 | ek sau painsath | 1 saikda (100) + 6 dahai (60) + 5 ikai |
| 999 | nau sau ninyaanve | 9 saikde (900) + 9 dahai (90) + 9 ikai |
| 1011 | ek hazaar gyaarah | 1 hazaar (1000) + 0 saikda + 1 dahai (10) + 1 ikai |
Round number mein chhota number add karna (place box rule): chhote number ko right se likho, yaani ikai ke neeche ikai, dahai ke neeche dahai. Phir har boxes mein jo hai, woh jawab mein utaar do. Ek digit wala number sirf ikai ka zero badalta hai, do digit wala ikai aur dahai dono.
- 100 + 65: 65 mein do digit, to 6 dahai mein aur 5 ikai mein: 1|6|5 = 165.
- 100 + 2: 2 sirf ikai mein, dahai ka 0 waise hi rehta hai: 1|0|2 = 102 (12 nahi, 120 nahi!).
- 200 + 6: 6 sirf ikai mein: 2|0|6 = 206.
- 1000 + 11: 11 mein do digit, to 1 dahai mein aur 1 ikai mein: 1|0|1|1 = 1011.
✖️ Multiply kya hai? (Multiplication)
Multiply (sign ×) matlab ek hi number ko baar-baar add karna. “6 × 4” ko bolte hain “6 times 4”, matlab 4 ko 6 baar add karo:
6 × 4 = 4 + 4 + 4 + 4 + 4 + 4 = 24
Isi tarah 6 × 7 matlab 7 ko 6 baar add karo. Running total (har baar ka naya sum) dekho: 7, 14, 21, 28, 35, 42. To 6 × 7 = 42.
10 dahai = 1 saikda: 10 dande (har danda 10) milkar 100 bante hain, yaani 1 saikda. Isliye 24 dahai = 20 dahai + 4 dahai = 2 saikde + 4 dahai = 240. (Aur 10 saikde milkar 1 hazaar, yaani 1000, bante hain.)
Pieces mein multiply kyun kar sakte hain? 47 = 4 dande (40) + 7 cube (7). 47 ko 6 baar lena matlab neeche jaisi 6 line. Dande alag gin lo, cube alag gin lo, total utna hi rahega:
6 × 47: 6 baar 40 = 240, 6 baar 7 = 42, total 240 + 42 = 282
Multiply mein carry 1 se bada ho sakta hai: sum mein carry aksar 1 hota hai, par multiply mein bada bhi aa sakta hai. Column mein 6 × 7 = 42 aaya, yaani 4 dahai aur 2 ikai. To ikai mein 2 likho aur 4 dahai carry karo (aage le jao). Phir dahai mein 6 × 4 = 24, usme carry ke 4 add karo: 24 + 4 = 28. Jawab 282.
Multiply mein jagah convert karo, jawab wahi: 16 × 4 aur 4 × 16 ek hi cheez hain. Neeche dots dekho: 4 line, har line mein 16 dots. Line se count karo to 4 baar 16; khade column se count karo to 16 baar 4. Dots wahi hain, to jawab bhi wahi: 64. Isliye jo aasaan lage, us tarah add karo.
Copy pe column mein (28 + 15 jaisa):
- Ikai: 6 × 7 = 42. Neeche ikai mein 2 likho. 42 ke 4 dahai carry hain: chhota 4 dahai wale digit (4) ke upar likho.
- Dahai: 6 × 4 = 24, usme upar likha carry 4 add karo: 24 + 4 = 28. Neeche 28 likho (8 dahai mein, 2 saikde mein).
- Jawab: 282.
10 se multiply: 3 × 10 matlab 10 ko 3 baar add karna: 10 + 10 + 10 = 30. Kisi number ko 10 se multiply karo to woh har digit ek jagah left shift jaata hai aur ikai mein 0 aa jaata hai: 3 → 30, 30 → 300.
🟦 Square kya hai? Chhota ² ka matlab (Chapter 6 yaad karo)
Kisi number ko usi number se multiply karna us number ka square (Hindi mein “varg”) kehlata hai. Ise number ke upar-right mein chhota ² likh kar dikhate hain. 7² padho “7 ka square” ya “7 square”, matlab 7 × 7 = 49. Dhyaan: 7² ka matlab 7 × 2 nahi hai (woh 14 hota)!
Name “square” kyun? Square ka ek matlab square bhi hai (jiski all four bhujaayein, yaani kinaare, equal hon). 7 line banao, har line mein 7 dots: dots ka ek square ban jaata hai, aur total dots 7 × 7 = 49. To 7² = 49 dots ka square.
| Square | Matlab | Jawab |
|---|---|---|
| 3² | 3 × 3 | 9 |
| 7² | 7 × 7 | 49 |
| 10² | 10 × 10 | 100 |
| 35² | 35 × 35 | 1225 (Post 6.1 ki trick) |
| 996² | 996 × 996 | 992016 (aaj ki trick!) |
Chapter 7 se relation: 996² bas 996 × 996 hai, yaani base method ka woh sawaal jisme dono numbers ek jaise hain. Isliye dono numbers base se utne hi door hote hain, aur trick aur bhi aasaan ho jaati hai.
📏 Base 1000 se kitna kam, kitna zyada?
Har number ke liye ek chhota sawaal: “Base tak pahunchne mein kitna bacha?” ya “Base se kitna aage nikal gaya?”
- Kitna kam (number base se chhota ho) = base − number. Matlab number ko base banne ke liye kitna aur chahiye.
- Kitna zyada (number base se bada ho) = number − base. Matlab number base se kitna aage hai.
1000 se kitna kam? Post 3.2 wali trick: pehle do digit ko 9 se poora karo, last ko 10 se. 1000 − 997: 9 − 9 = 0, 9 − 9 = 0, 10 − 7 = 3 → 003, yaani 3. 1000 − 988: 9 − 9 = 0, 9 − 8 = 1, 10 − 8 = 2 → 012, yaani 12.
| Number | Base 1000 se | Kaise nikala |
|---|---|---|
| 998 | 2 kam | 1000 − 998 = 2 |
| 996 | 4 kam | 0, 0, 10 − 6 = 4 → 004 |
| 989 | 11 kam | 0, 9 − 8 = 1, 10 − 9 = 1 → 011 |
| 1004 | 4 zyada | 1004 − 1000 = 4 |
| 1012 | 12 zyada | 1012 − 1000 = 12 |
Chhota path: 1000 se zyada wale (1001 se 1050 jaise) ka “kitna zyada” = uske last teen digit: 1004 → 004 = 4.
🧱 Wall ( | ), right part ke digit, aur carry
Is trick mein jawab do parts mein banta hai: left part | right part. Beech ki khadi lakeer ( | ) ko “wall” samjho. Yeh sirf hamare samjhne ke liye hai; asli jawab mein wall nahi likhte, dono parts saath-saath likh dete hain.
Base 1000 mein 3 zero hain. Isliye left part kitne hazaar count karta hai, aur right part ko jawab mein teen boxes milte hain. Rule:
Right parts mein digit = base ke zero (3)
- Right chhota pade (kam digit) → aage 0 bharo.
- Right bada pade (zyada digit) → sabse left wala extra part left part mein add karo (carry).
- 993 | 012: 12 ko teen digit mein likho: 012. 993 hazaar + 12 = 993000 + 12 = 993012.
- 995 | 006: 6 ko 006 likho. 995000 + 6 = 995006.
- Carry: maan lo kisi sawaal mein 979 | 1452 aaya: chaar digit, jagah teen. 1452 = 1 hazaar + 452 → 979 + 1 = 980 → 980452. Pakka: 979000 + 1452 = 980452 ✅.
Pehle multiply, phir sum (zaroori rule): jab ek hi line mein × aur + dono hon, to pehle × (multiply) karo, phir + (sum). Jaise 5 × 10 + 6: pehle 5 × 10 = 50, phir 50 + 6 = 56. (Agar pehle 10 + 6 = 16 karke 5 × 16 karte to 80 aata, jo galat hai.) Is post mein “left × base + right” isi rule se padhna.
🔢 Bahut bade numbers padhna: hazaar, lakh, das lakh
Place value ki jagahein right se aage increase hoti rehti hain, har agli jagah pichhli se 10 times: Ikai (1), Dahai (10), Saikda (100), Hazaar (1000), Das hazaar (10000), Lakh (100000, yaani 100 hazaar), Das lakh (1000000).
| Number | Kaise padhein | Pieces |
|---|---|---|
| 993012 | nau lakh teeraanve hazaar baarah | 993 hazaar + 12 = 993000 + 12 |
| 995006 | nau lakh pachaanve hazaar chhe | 995000 + 6 |
| 1010024 | das lakh das hazaar chaubees | 1010 hazaar + 24 = 1010000 + 24 |
Teen-teen ka group: bade jawab ko right se teen-teen digit mein dekho: 993 | 012. Right ka group hazaar se chhota part hai (0 se 999), aur left ka group batata hai “kitne hazaar”. Base 1000 ki trick mein wall bilkul yahin aati hai!
Hazaar se multiply: 1000 = 10 × 10 × 10, isliye 1000 se multiply = peeche teen 0: 993 × 1000 = 993000.
🔵 Round number ka square: 30², 400²
30 = 3 × 10. To 30² = 30 × 30 = 3 × 10 × 3 × 10. Multiply mein jagah badal sakte hain (“Multiply kya hai?” box), to pehle 3 × 3 = 9, phir 10 × 10 = 100: 9 × 100 = 900.
Rule: digit ka square, phir peeche zero double
| Square | Digit ka square | Zero | Jawab |
|---|---|---|---|
| 30² | 3 × 3 = 9 | 1 zero → 2 zero | 900 |
| 50² | 5 × 5 = 25 | 1 zero → 2 zero | 2500 |
| 400² | 4 × 4 = 16 | 2 zero → 4 zero | 160000 |
(160000 padho “ek lakh saath hazaar”.) Dhyaan: 30² = 900, 90 nahi aur 9000 nahi.
🔁 Chhota sa warm-up
- 1000 − 993 = ?
- 7² = ?
- 986 × 1000 + 49 = ?
Answers dekho
- 7
- 49
- 986049 (pehle multiply, phir sum)
Teeno aa gaye? Yahi milkar 993² = 986049 banta hai (993 − 7 = 986, right 049)!
— 📌 charumam.com
🎬 Story: Hazaar Ki Lineup
Annual function mein square lineup banana tha: 996 line, har line mein 996 kursi. Principal ma’am ne poocha: “Total kitni kursiyaan?”
Simran boli: “Ma’am, 996 to 1000 se 4 kam. 996 − 4 = 992. Aur 4 × 4 = 16, par base 1000 mein teen boxes, to 016.”
Phir Simran ne poora jawab bola: “992 aur 016 saath likho: 992016 kursiyaan, yaani nau lakh baanve hazaar solah!” Ma’am muskuraayin: “Itni kursiyaan to poore city mein nahi hongi, par calculation bilkul sahi hai!” 😄
Aaj base 1000 aur ek mix: kaunsa square kis trick se. 🎯
— 📌 charumam.com
🪄 Trick Step by Step: Base 1000: Right 3 Boxes, Aur Trick Chuno
💡 Is post ki ek badi baat: Base 1000 mein bhi wahi: left = number − deficit (ya + zyada), right = distance × distance, par 3 boxes mein (16 → 016, 9 → 009). Mix mein pehle number ko identify karo: base ke paas? 5 pe khatam? round? warna seedha multiply.
Step 1: Base chuno, zero count karo
996²: 996 sabse zyada 1000 ke paas. Base 1000, 3 zero, right ko 3 boxes.
Step 2: Deficit ya zyada
1000 − 996 = 4 kam (Post 3.2: 9 − 9 = 0, 9 − 9 = 0, 10 − 6 = 4 → 004).
Step 3: Left
Kam hai, to subtract karo: 996 − 4 = 992.
Step 4: Right, 3 boxes mein
4² = 4 × 4 = 16. Do digit, boxes teen: aage ek 0 → 016.
Step 5: Saath likho, padho
992 | 016 → 992016. Pehle multiply, phir sum: 992 × 1000 + 16 = 992000 + 16 = 992016 ✅. Padho: nau lakh baanve hazaar solah.
Base se zyada wala: 1007²
1007² (base 1000): 1007 − 1000 = 7, yaani 7 zyada. Left: wahi zyada add karo: 1007 + 7 = 1014. Right: 7² = 7 × 7 = 49. Base 1000 mein right ko 3 boxes chahiye, to aage 0 bharo: 049. Jawab: 1014 | 049 → 1014049.
Ek nazar mein: base 1000
| Square | Base se distance | Left | Right (distance²) | Jawab |
|---|---|---|---|---|
| 999² | 1 kam | 999 − 1 = 998 | 1 × 1 = 1 | 998 | 001 → 998001 |
| 998² | 2 kam | 998 − 2 = 996 | 2 × 2 = 4 | 996 | 004 → 996004 |
| 997² | 3 kam | 997 − 3 = 994 | 3 × 3 = 9 | 994 | 009 → 994009 |
| 995² | 5 kam | 995 − 5 = 990 | 5 × 5 = 25 | 990 | 025 → 990025 |
| 990² | 10 kam | 990 − 10 = 980 | 10 × 10 = 100 | 980 | 100 → 980100 |
| 988² | 12 kam | 988 − 12 = 976 | 12 × 12 = 144 | 976 | 144 → 976144 |
| 1001² | 1 zyada | 1001 + 1 = 1002 | 1 × 1 = 1 | 1002 | 001 → 1002001 |
| 1003² | 3 zyada | 1003 + 3 = 1006 | 3 × 3 = 9 | 1006 | 009 → 1006009 |
| 1005² | 5 zyada | 1005 + 5 = 1010 | 5 × 5 = 25 | 1010 | 025 → 1010025 |
| 1012² | 12 zyada | 1012 + 12 = 1024 | 12 × 12 = 144 | 1024 | 144 → 1024144 |
(988² aur 1012² mein right 144 hai: teen digit, aur boxes bhi teen. To carry nahi! Base 100 mein 144 pe carry aata tha, base 1000 mein nahi, kyunki jagah zyada hai.)
Mix: kaunsi trick kab?
| Number kaisa hai? | Example | Trick | Jawab |
|---|---|---|---|
| 10, 100 ya 1000 ke paas | 97², 104², 996² | Base method (Ch 13) | 9409, 10816, 992016 |
| 5 pe khatam | 65² | Chapter 6: 6 × 7 = 42, peeche 25 | 4225 |
| Round (peeche 0) | 30², 400² | Digit ka square, zero double | 900, 160000 |
| Kisi ke paas nahi | 67² | Seedha multiply (column) | 4489 |
(95² aur 105² do jagah fit hote hain: base ke paas bhi aur 5 pe khatam bhi. Dono method same jawab dete hain: 9025, 11025.)
🆘 Atak gaye? Aise socho
- Teen boxes: base 1000 → right 3 digit. 16 → 016, 4 → 004.
- Carry kab? Sirf tab jab right 1000 ya zyada (distance 32 ya zyada). Mangoes taur pe nahi.
- Kam ya zyada? 1000 se chhota → subtract karo. Bada → add karo.
- Padhna: right se teen-teen digit ka group: 992 | 016.
- Trick chuno: paas? 5? round? warna seedha.
— 📌 charumam.com
🔍 Yeh Kaam Kyun Karta Hai?
Chitra wahi, bas bada: 996² matlab 996 × 996 ka square. 4 column ki patti cut karo (bache 992), upar lagao (oonchai 996 + 4 = 1000). Box 992 × 1000 = 992000, baahar nikla corner 4 × 4 = 16.
Right ko 3 boxes kyun? Left part 992 asal mein 992 hazaar hai (992 × 1000). Hazaar se chhote saare parts (saikda, dahai, ikai) right ke paas hain: 3 jagah. 16 to sirf dahai aur ikai bharta hai, isliye saikde mein 0: 016.
Neeche chitra (measurement se nahi, samjhane ke liye):
Trick chunne ka map
— 📌 charumam.com
✏️ Solved Examples (Har Ek Normal Method Se Check)
Example 1: 999² = ?
999² (base 1000): 1000 − 999 = 1, yaani 1 kam. Left: wahi deficit subtract karo: 999 − 1 = 998. Right: 1² = 1 × 1 = 1. Base 1000 mein right ko 3 boxes chahiye, to aage 0 bharo: 001. Jawab: 998 | 001 → 998001.
✔️ Normal method se check: 999 × 1000 = 999000, phir 999 subtract karo: 999000 − 999 = 998001 ✅ (Chapter 10)
Example 2: 1012² = ?
1012² (base 1000): 1012 − 1000 = 12, yaani 12 zyada. Left: wahi zyada add karo: 1012 + 12 = 1024. Right: 12² = 12 × 12 = 144 (3 boxes, poore bhar gaye). Jawab: 1024 | 144 → 1024144.
(12 × 12 = 144: 12 ko 10 baar 120, 2 baar 24, total 144.)
✔️ Normal method se check: 1012 × 1000 = 1012000, 1012 × 12 = 12144 (1000 × 12 = 12000, 12 × 12 = 144, 12000 + 144 = 12144), phir 1012000 + 12144 = 1024144 ✅
Example 3: 95² = ? (do methods se)
95² (base 100): 100 − 95 = 5, yaani 5 kam. Left: wahi deficit subtract karo: 95 − 5 = 90. Right: 5² = 5 × 5 = 25 (2 boxes, poore bhar gaye). Jawab: 90 | 25 → 9025.
Chapter 6 se: last 5 remove karo → 9. 9 × 10 = 90, peeche 25 → 9025. Same!
✔️ Normal method se check: 95 × 95 = 9500 − 475 = 9025 ✅ (95 ko 100 baar = 9500, phir 95 × 5 = 475 subtract karo, kyunki 95 to 100 se 5 kam. 95 × 5 = 90 × 5 + 5 × 5 = 450 + 25 = 475)
Example 4: 40² = ? (round)
Digit 4 ka square: 4 × 4 = 16. 40 mein ek 0, square mein do 0: 1600.
✔️ Normal method se check: 40 × 40 = 4 × 4 × 100 = 16 × 100 = 1600 ✅
— 📌 charumam.com
💡 CharuMam Ki Smart Trick
Post 13.1 wali Base Wala Square trick kisi bhi base pe chalti hai: 10, 100, 1000, 10000. Bas right part ke boxes base ke zero jitne. Aur trick chunne ka CharuMam rule hai “Pehle Dekho” (dekh kar identify karo): pehle number ko dekho, phir sabse chhota path lo.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Trick use karein? | Kyun |
|---|---|---|
| 990 se 1010 (996², 1007²) | ✅ Base 1000 | Right 3 boxes, carry kam hi aata hai. |
| 65², 85² (5 pe khatam) | ✅ Chapter 6 | Aage wala × agla, peeche 25. |
| 30², 400² (round) | ✅ Zero rule | Digit ka square, zero double. |
| 67², 43² (kisi ke paas nahi) | ⚠️ Seedha multiply | Base method ki distance bahut badi. |
| 95², 105² | ✅ Dono | Base aur Chapter 6, dono 9025 / 11025. |
| 500 ke paas (498²) | ❌ Abhi nahi | 500 jaisa base is chapter mein nahi; abhi seedha multiply karo. |
— 📌 charumam.com
❌→✅ Common Mistakes
Mistake 1: Base 1000 mein sirf 2 boxes
Sawaal: 996²
❌ Galat: 992 | 16 → 99216.
✅ Sahi: 3 boxes: 016 → 992016. Estimate: 996² lagbhag 1000 × 1000 = 1000000 (das lakh), to 6 digit chahiye.
Mistake 2: Base 100 jaisa carry kar diya
Sawaal: 988²
❌ Galat: 976 | 144 → 977 | 44 → 97744.
✅ Sahi: base 1000 mein right ke 3 boxes, 144 fit ho jaata hai: 976144.
Mistake 3: Round square mein ek hi 0
Sawaal: 30²
❌ Galat: 90.
✅ Sahi: 30 × 30: 3 × 3 = 9, aur 10 × 10 = 100 → 900.
Mistake 4: Door wale number pe base method
Sawaal: 67²
❌ Galat: base 100, 33 kam: 34 | 1089 → … bahut long, aur mistake ka darr.
✅ Sahi: seedha column. 67 × 7: 7 × 7 = 49 → 9 likho, 4 carry; 7 × 6 = 42, 42 + 4 = 46 → 469. 67 × 60: pehle 67 × 6: 6 × 7 = 42 → 2 likho, 4 carry; 6 × 6 = 36, 36 + 4 = 40 → 402, phir peeche 0 → 4020. Add karo: 469 + 4020 = 4489.
🧠 Rule of thumb: Base 1000 → right 3 boxes. Aur pehle trick chuno: paas → base, 5 → Chapter 6, round → zero double, baaki → seedha.
— 📌 charumam.com
🏃 Speed Drill: 15 Sawaal, Timer Ke Saath
Timer lagao. 15 mix square. Target: 6 minute. Har sawaal se pehle bolo: “kaunsi trick?”
- 999² = ?
- 998² = ?
- 997² = ?
- 996² = ?
- 995² = ?
- 1001² = ?
- 1002² = ?
- 1003² = ?
- 1004² = ?
- 1005² = ?
- 1008² = ?
- 990² = ?
- 30² = ?
- 95² = ?
- 65² = ?
Mera time: ______ · Sahi: ____ / 15
Answers dekho (pehle khud karo!)
- 998001
- 996004
- 994009
- 992016
- 990025
- 1002001
- 1004004
- 1006009
- 1008016
- 1010025
- 1016064
- 980100
- 900
- 9025
- 4225
Kaise kiya (kuch):
990² (base 1000): 1000 − 990 = 10, yaani 10 kam. Left: wahi deficit subtract karo: 990 − 10 = 980. Right: 10² = 10 × 10 = 100 (3 boxes, poore bhar gaye). Jawab: 980 | 100 → 980100.
65²: Chapter 6: 6 × 7 = 42, peeche 25 → 4225.
— 📌 charumam.com
⏰ One-Minute Challenge
Sirf 1 minute (60 second). Timer lagao, aur jitne ho sakein utne sawaal mann mein (bina copy ke) karo. Sirf jawab likhna hai.
- 999² = ?
- 1001² = ?
- 998² = ?
- 1002² = ?
- 997² = ?
- 1003² = ?
- 996² = ?
- 1004² = ?
- 20² = ?
- 40² = ?
| Rating | Kitne sahi, kitne time mein |
|---|---|
| 🌱 Beginner | 60 second mein 5 se 7 sahi. Badhiya start! |
| 🚀 Pro | 60 second mein 8 ya 9 sahi |
| 🏆 Champion | 10 mein 10 sahi, 60 second ke andar |
Answers dekho
- 998001
- 1002001
- 996004
- 1004004
- 994009
- 1006009
- 992016
- 1008016
- 400
- 1600
Dhyaan: 20²: 2 × 2 = 4, phir do 0 → 400. 1004²: 1008 | 016 → 1008016.
5 se kam sahi? Koi baat nahi! Trick wala section ek baar aur padho aur kal phir try karo. Har day thoda better, bas yahi chahiye. 💪
— 📌 charumam.com
📝 10 MCQs (Har Option Ka Reason)
MCQ matlab ek sawaal ke chaar jawab (options) diye hote hain, unme se ek sahi chunna hai.
Q1. 996² = ?
Jawab aur reason dekho
Sahi jawab: (c) 992016
- (a) galat ❌: 992160: 16 ke aage ki jagah peeche 0 laga diya.
- (b) galat ❌: 1000016: left mein deficit add kar di (996 + 4 = 1000 → 1000 | 016).
- (c) sahi ✅: 4 kam: 992 | 016 → 992016.
- (d) galat ❌: 99216: base 1000 mein sirf 2 boxes diye (16).
Q2. 1007² = ?
Jawab aur reason dekho
Sahi jawab: (b) 1014049
- (a) galat ❌: 1007049: left mein zyada add karna bhool gaye (1007 | 049).
- (b) sahi ✅: 7 zyada: 1014 | 049 → 1014049.
- (c) galat ❌: 101449: sirf 2 boxes (49).
- (d) galat ❌: 1014490: 0 aage ki jagah peeche.
Q3. Base 1000 wale square mein right ke kitne boxes?
Jawab aur reason dekho
Sahi jawab: (a) 3
- (a) sahi ✅: 1000 mein 3 zero.
- (b) galat ❌: 2 boxes base 100 mein.
- (c) galat ❌: 1 box base 10 mein.
- (d) galat ❌: 4 boxes base 10000 mein.
Q4. 999² = ?
Jawab aur reason dekho
Sahi jawab: (d) 998001
- (a) galat ❌: 99801: base 1000 mein sirf 2 boxes diye (998 | 01).
- (b) galat ❌: 998100: 1 ko 001 ki jagah 100 likha.
- (c) galat ❌: 1000001: left mein deficit add kar di (999 + 1 = 1000 → 1000 | 001).
- (d) sahi ✅: 1 kam: 998 | 001 → 998001.
Q5. 988² = ?
Jawab aur reason dekho
Sahi jawab: (c) 976144
- (a) galat ❌: 977044: 144 ka 1 left mein bhej diya (977 | 044); base 1000 mein 144 teen boxes mein poora aata hai, carry ki zaroorat nahi.
- (b) galat ❌: 1000144: left mein deficit add kar di (988 + 12 = 1000 → 1000 | 144).
- (c) sahi ✅: 12 kam: 976 | 144 → 976144 (3 boxes, carry nahi).
- (d) galat ❌: 97744: base 100 jaisa sirf 2 boxes diye, to 144 ka 1 left mein chala gaya (976 + 1 = 977 → 977 | 44).
Q6. 85² ke liye sabse aasaan trick?
Jawab aur reason dekho
Sahi jawab: (b) Chapter 6 (8 × 9, peeche 25)
- (a) galat ❌: 85 round number nahi.
- (b) sahi ✅: 8 × 9 = 72, peeche 25 → 7225.
- (c) galat ❌: Base 100 se 15 door: chalta hai par long (70 | 225; 225 = 200 + 25, to 2 saikde left mein → 72 | 25).
- (d) galat ❌: 85, 1000 se bahut door.
Q7. 30² = ?
Jawab aur reason dekho
Sahi jawab: (a) 900
- (a) sahi ✅: 3 × 3 = 9, zero double → 900.
- (b) galat ❌: 90: sirf ek 0 lagaya.
- (c) galat ❌: 9000: teen 0 laga diye.
- (d) galat ❌: 60: 30 × 2 kar diya (double, square nahi).
Q8. 1012² = ?
Jawab aur reason dekho
Sahi jawab: (d) 1024144
- (a) galat ❌: 102544: base 100 jaisa sirf 2 boxes diye, to 144 ka 1 left mein chala gaya (1024 + 1 = 1025 → 1025 | 44).
- (b) galat ❌: 1025044: carry bheja, zaroorat nahi thi.
- (c) galat ❌: 1012144: left mein zyada add karna bhool gaye (1012 | 144).
- (d) sahi ✅: 12 zyada: 1024 | 144 → 1024144.
Q9. Kis square ke liye base method theek NAHI?
Jawab aur reason dekho
Sahi jawab: (c) 67²
- (a) galat ❌: 1003², 1000 se 3 zyada: 1006009.
- (b) galat ❌: 12², 10 se 2 zyada: 144.
- (c) sahi ✅: 67 kisi base ke paas nahi (100 se 33 door): seedha multiply.
- (d) galat ❌: 97², 100 se 3 kam: 9409.
Q10. 95² = ?
Jawab aur reason dekho
Sahi jawab: (b) 9025
- (a) galat ❌: 9525: left mein deficit ghatai hi nahi (95 | 25).
- (b) sahi ✅: Base: 90 | 25. Chapter 6: 9 × 10 = 90, peeche 25.
- (c) galat ❌: 9010: right mein 5 × 2 = 10 kiya (double, square nahi) → 90 | 10.
- (d) galat ❌: 10025: left mein deficit add kar di (95 + 5 = 100 → 100 | 25).
— 📌 charumam.com
🧠 Challenge: HOTS Aur Olympiad Style
HOTS matlab Higher Order Thinking Skills, yaani aise sawaal jinme sirf trick nahi, thoda mind bhi lagana padta hai. Olympiad ek maths competition (pratiyogita) hota hai.
Q1. 99² = 9801, 999² = 998001. 9999² kya hoga? (base 10000, right 4 boxes)
Solution dekho
9999 → 1 kam. Left 9999 − 1 = 9998. Right 1 × 1 = 1 → 4 boxes: 0001. Jawab 9998 | 0001 → 99980001. Pattern: 9 ki count ek kam, phir 8, phir utne 0, phir 1: 9998 | 0001 = teen 9, phir 8, phir teen 0, phir 1.
Check: 9999 × 10000 − 9999 = 99990000 − 9999 = 99980001 ✅
Q2. 997² aur 1003² mein kitna difference?
Solution dekho
997² → 994 | 009 → 994009. 1003² → 1006 | 009 → 1006009. Right same (009), left mein 1006 − 994 = 12. To difference 12 hazaar = 12000.
Check: 1006009 − 994009 = 12000 ✅
Q3. Reverse: kisi number ka square 1006009 hai, aur number 1000 ke paas hai. Number?
Solution dekho
Right 009 = 3 × 3, to distance 3. Left 1006 hazaar, 1000 se bada, to number base se zyada wala: 1000 + 3 = 1003. Check left: 1003 + 3 = 1006 ✅.
Check: 1003² = 1006009 (base se zyada wala HOTS) ✅
Q4. Ek square park ki bhuja 50 metre. Area? Aur agar bhuja 500 metre ho?
Solution dekho
50²: 5 × 5 = 25, zero double → 2500 square metre (square metre area ki ikai: 1 metre long aur 1 metre chaudi square jagah; metre length ki ikai hai, lagbhag ek bade step jitni). 500²: 5 × 5 = 25, phir 4 zero → 250000 square metre (dhaai lakh, yaani 2 lakh 50 hazaar).
Check: 500 × 500 = 5 × 5 × 100 × 100 = 25 × 10000 = 250000 ✅
— 📌 charumam.com
🎯 Exam Mein Kahan Kaam Aayega?
| Exam | Kahan kaam aayega |
|---|---|
| School exam (Class 6–8) | Squares, area, bade numbers padhna (lakh). |
| Maths Olympiad | Pattern (99², 999², 9999²), difference wale sawaal. |
| NTSE / MAT | Number series, trick chunne wale sawaal. |
| SSC / Bank (aage) | Simplification: 996², 1012² turant. |
Shabdon ka matlab: Olympiad = school ke students ki maths pratiyogita (competition). NTSE = Class 10 ke students ka ek national scholarship (vazifa) exam. MAT = Mental Ability Test, yaani sochne-samajhne ki pariksha (NTSE ka ek part). SSC / Bank exam = badon ke government naukri ke exam. Simplification = long calculation ko chhota karke jawab nikaalna. Number series = numbers ki ek line jo kisi rule se aage increase hoti hai, aur agla number batana hota hai. Jaise 5, 10, 15, 20, … mein har baar 5 jud raha hai, to agla 25. Class 6–8 = school ki chhathi se aathvi kaksha.
— 📌 charumam.com
👩🏫 CharuMam Ka Tip
Mantra: “base dekho, zero count karo, boxes bharo.” Aur koi bhi square dekho to pehle 2 second socho: “paas, paanch, round, ya seedha?” Agla post: Chapter 13 ke tricky sawaal! 🎯
— 📌 charumam.com
⏱ After Timer: Ab Trick Se!
Wahi sawaal jo shuru mein kiya tha. Stopwatch phir chalu kijiye, aur is baar aaj ki trick se kijiye:
Trick se kaise karein (dekho)
996, base 1000 se 4 kam. Left: 996 − 4 = 992. Right: 4 × 4 = 16 → 3 boxes → 016. Jawab 992 | 016 → 992016 ✅
| Before time | After time | Kitna tez? |
|---|---|---|
| ____ second | ____ second | Before − After = ____ second bache! |
Pehli baar mein time zyada bhi lag sakta hai, ghabraiye nahi! Nayi trick ko 3 se 4 days ki practice chahiye. Phir yeh purane method se kaafi tez ho jaati hai. 🚀
— 📌 charumam.com
🤖 Aur Practice: AI Tutor Se Poochho
Neeche wali line copy kijiye aur CharuMam AI Tutor (tutor.charumam.com) mein paste kar dijiye. Tutor aapko naye sawaal dega aur mistake hone pe samjhayega:
— 📌 charumam.com
❓ FAQs (Students Ke Asli Sawaal)
1. Base 1000 mein carry kab aayega?
Jab distance ka square 1000 ya zyada ho: distance 32 ya zyada (31 × 31 = 961, 1000 se kam; 32 × 32 = 1024, 1000 se zyada). Itni door ke number pe yeh trick waise bhi aasaan nahi.
2. 992016 kaise padhein?
Nau lakh baanve hazaar solah. Teen-teen ke group: 992 | 016.
3. 95² ke liye kaunsi trick?
Dono: base (90 | 25) ya Chapter 6 (9 × 10 = 90, peeche 25).
4. 500 ke paas wale (498²)?
Is chapter ke base sirf 10, 100, 1000 hain. Abhi aise square seedha multiply se karo.
5. Agle post mein kya hai?
Post 13.4: Chapter 13 ke tricky sawaal.
— 📌 charumam.com
🟢 Recap: Aaj Kya Seekha
- Base 1000: right 3 boxes (16 → 016).
- 996² = 992016, 1007² = 1014049.
- Base 1000 mein 144 pe carry nahi.
- Round: 30² = 900 (zero double).
- 5 pe khatam: Chapter 6.
- Pehle trick chuno, phir calculation.
— charumam.com 🎯
👉 Aage Kya?
Ab Chapter 13 ka last post: tricky sawaal. Reverse sawaal (kis number ka square 9409?), difference, pattern aur dhokhe!
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬
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- 🌐 Website: charumam.com
- 🤖 AI Tutor (doubt poochho, 24×7): tutor.charumam.com
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