Chapter 6 ka aakhri post! Aaj 6.1–6.3 ka mix: ulte sawaal (square diya hai, number dhoondo), pattern (squares ki seedhi), dhokhe (36², 45 × 55, jahan trick nahi lagti) aur area wale word problems. Har sawaal mein pehle shart check, phir trick, phir check.
⏱ Before Timer: Pehle Purane Tareeke Se
Pehle seedha tareeka. 45² + 55² matlab 45 × 45 aur 55 × 55 nikaal kar jodo.
- 45 × 45: 45 ko 40 baar = 450 ko 4 baar: 450, 900, 1350, 1800. 45 ko 5 baar = 450 ka aadha = 225. Kul 1800 + 225 = 2025.
- 55 × 55: 55 ko 50 baar = 5500 ka aadha (Post 5.3) = 2750. 55 ko 5 baar = 550 ka aadha = 275. Kul 2750 + 275 = 3025.
- Jodo: 2025 + 3025 = 5050.
(5050! Yaad hai Post 2.4 mein 1 se 100 tak ka jod bhi 5050 tha? 😊)
Ab phone ya ghadi mein stopwatch (samay naapne wali ghadi) chalu kijiye. Neeche wala sawaal isi school wale tareeke (column method) se kijiye, copy-pencil ke saath. Column method na aata ho to ungliyon pe gin kar bhi kar sakte hain. Jaise hi jawab mil jaaye, stopwatch rok dijiye aur apna time likh lijiye.
Mera time: ______ second
Jawab dekho
45² + 55² = 5050
Abhi trick nahi dekhni! Post ke end mein After Timer mein yahi sawaal trick se karenge aur dono time ki tulna karenge. 😊
— 📌 charumam.com
✅ Pehle Yeh Aata Hai
Aaj ke tools: Post 6.1 (35² trick), 6.2 (3-digit, 11 × 12 jaise guna), 6.3 (43 × 47 bahan-trick), aur Ch 5 ka aadha karna. Neeche boxes ek baar aur. Naye shabd:
📖 Shabd jo is post mein aayenge
- Ulta sawaal: square diya hai (jaise 4225), number dhoondhna hai. Peeche ka 25 hatao, bache number ko “kaun × agla” mein todo.
- Pattern (seedhi): 15², 25², 35² … ke jawab ek niyam se badhte hain: farq 400, 600, 800, … har baar 200 zyada.
- Farq: bade mein se chhota ghatana: 1225 − 625 = 600.
- Dhokha: sawaal jo trick jaisa dikhe par shart poori na ho: 36² (5 pe khatam nahi), 45 × 55 (dahai alag).
- Kshetrafal (area): kisi jagah ke andar kitni 1 × 1 wali tile aayengi. Chaukor: bhuja × bhuja. Aayat: lambai × chaudai.
- Varg metre: area ki ikai: 1 metre lambi, 1 metre chaudi tile jitni jagah.
📏 Bade numbers padhna aur round number mein jodna
Har digit ki ek jagah (place) hoti hai. Right se gino: 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 guna 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 jodna (place box niyam): chhote number ko right se likho, yaani ikai ke neeche ikai, dahai ke neeche dahai. Phir har dabbe 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.
✖️ Guna kya hai? (Multiplication)
Guna (nishaan ×) matlab ek hi number ko baar-baar jodna. “6 × 4” ko bolte hain “6 guna 4”, matlab 4 ko 6 baar jodo:
6 × 4 = 4 + 4 + 4 + 4 + 4 + 4 = 24
Isi tarah 6 × 7 matlab 7 ko 6 baar jodo. Running total (har baar ka naya jod) 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.)
Tukdon mein guna 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, kul utna hi rahega:
6 × 47: 6 baar 40 = 240, 6 baar 7 = 42, kul 240 + 42 = 282
Guna mein carry 1 se bada ho sakta hai: jod mein carry aksar 1 hota hai, par guna 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 jodo: 24 + 4 = 28. Jawab 282.
Guna mein jagah badlo, jawab wahi: 16 × 4 aur 4 × 16 ek hi cheez hain. Neeche dots dekho: 4 line, har line mein 16 dots. Line se gino to 4 baar 16; khade column se gino to 16 baar 4. Dots wahi hain, to jawab bhi wahi: 64. Isliye jo aasaan lage, us tarah jodo.
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 jodo: 24 + 4 = 28. Neeche 28 likho (8 dahai mein, 2 saikde mein).
- Jawab: 282.
10 se guna: 3 × 10 matlab 10 ko 3 baar jodna: 10 + 10 + 10 = 30. Kisi number ko 10 se guna karo to woh har digit ek jagah left khisak jaata hai aur ikai mein 0 aa jaata hai: 3 → 30, 30 → 300.
💯 100 se guna = peeche do 0 lagao
100 = 10 × 10 (10 ko 10 baar jodo: 10, 20, 30, … 100). Isliye 100 se guna karna matlab do baar 10 se guna. Har baar 10 se guna pe peeche ek 0 lagta hai (upar wala box), to 100 se guna pe do 0:
36 → (× 10) 360 → (× 10) 3600
Place value se: 36 × 100 matlab 36 saikde (36 sau). 36 sau = 3600 (padho: teen hazaar chhe sau).
| Number | × 100 |
|---|---|
| 7 | 700 |
| 36 | 3600 |
| 37 | 3700 |
| 124 | 12400 (padho: barah hazaar chaar sau) |
Bade number padhna: 12400 mein right se paanchvi jagah Das hazaar (10000 wale) hai. 12400 = 1 das hazaar + 2 hazaar + 4 saikde, yaani 10000 + 2000 + 400.
🟦 Square kya hai? Chhota ² ka matlab
Kisi number ko usi number se guna karna us number ka square (Hindi mein “varg”) kehlata hai. Ise number ke upar-right mein chhota ² likh kar dikhate hain. 5² padho “5 ka square” ya “5 square”, matlab 5 × 5 = 25. Dhyaan: 5² ka matlab 5 × 2 nahi hai (woh 10 hota)!
Naam “square” kyun? Square ka ek matlab hai chaukor (jiski chaaron bhujaayein barabar hon). 5 line banao, har line mein 5 dots: dots ka ek chaukor ban jaata hai, aur kul dots 5 × 5 = 25. To 5² = 25 dots ka chaukor.
| Square | Matlab | Jawab |
|---|---|---|
| 3² | 3 × 3 | 9 |
| 5² | 5 × 5 | 25 |
| 10² | 10 × 10 | 100 |
| 35² | 35 × 35 | 1225 (Post 6.1) |
➕1 Number × agla number (1 se 9 tak)
Aaj ki trick mein ek chhota guna baar-baar aayega: ek number × uske theek baad wala (agla) number. 3 ka agla number 4 hai (3 + 1 = 4). 8 ka agla 9. Neeche poori table hai. Har guna ko baar-baar jod se bhi nikaal sakte ho (GUNA box): 3 × 4 matlab 4 ko 3 baar jodo.
| Number × agla | Baar-baar jod se | Jawab |
|---|---|---|
| 1 × 2 | 2 | 2 |
| 2 × 3 | 3 + 3 | 6 |
| 3 × 4 | 4 + 4 + 4 | 12 |
| 4 × 5 | 5 + 5 + 5 + 5 | 20 |
| 5 × 6 | 6 + 6 + 6 + 6 + 6 | 30 |
| 6 × 7 | 7, 14, 21, 28, 35, 42 (running total) | 42 |
| 7 × 8 | 8, 16, 24, 32, 40, 48, 56 | 56 |
| 8 × 9 | 9, 18, 27, 36, 45, 54, 63, 72 | 72 |
| 9 × 10 | 9 ke peeche 0 (10 se guna) | 90 |
Pattern dekho: 2, 6, 12, 20, 30, 42, 56, 72, 90. jodne wala number har baar 2 badhta hai: 4, 6, 8, 10, 12, 14, 16, 18. (6 + 6 = 12, 12 + 8 = 20, 20 + 10 = 30, …) Yeh pattern bhool jaao to bhi chalega; table ya baar-baar jod kaafi hai.
➕1 Bade number × agla number (10 se 19 tak)
3-digit square ke liye 10 × 11, 11 × 12, 12 × 13 … chahiye. Inhe tukdon mein todo (GUNA box wali soch): 13 = 10 + 3, to 12 × 13 matlab: 12 ko 10 baar, aur 12 ko 3 baar. 12 ko 10 baar = 120 (peeche 0). 12 ko 3 baar = 12 + 12 + 12 = 36. Kul 120 + 36 = 156.
| Number × agla | Tukdon mein | Jawab |
|---|---|---|
| 10 × 11 | 11 ke peeche 0 (10 se guna) | 110 |
| 11 × 12 | 110 + 22 (11 ko 10 baar, 11 ko 2 baar) | 132 |
| 12 × 13 | 120 + 36 | 156 |
| 13 × 14 | 130 + 52 (13 ko 4 baar: 13, 26, 39, 52) | 182 |
| 14 × 15 | 140 + 70 (14 ko 5 baar = 140 ka aadha) | 210 |
| 15 × 16 | 150 + 90 (15 ko 6 baar: 15, 30, 45, 60, 75, 90) | 240 |
| 16 × 17 | 160 + 112 (16 ko 7 baar) | 272 |
| 17 × 18 | 170 + 136 (17 ko 8 baar) | 306 |
| 18 × 19 | 180 + 162 (18 ko 9 baar) | 342 |
| 19 × 20 | 19 ko 2 baar = 38, phir peeche 0 | 380 |
Ch 4 se ek chhota raasta: 11 × 12 aur 12 × 11 same hain (jagah badlo, jawab wahi). 12 × 11 ki trick: 1 | 1 + 2 | 2 = 132. ✅
🔁 Chhota sa warm-up
- 45² = ?
- 56 = kaun × agla?
- 1225 − 625 = ?
Answers dekho
- 2025 (4 × 5 = 20, peeche 25)
- 7 × 8
- 600
Tools tayyar! Ab tricky sawaal.
— 📌 charumam.com
🎬 Kahani: Quiz Competition Ka Final Round
School quiz ka final round. Quiz master: “Kis number ka square 4225 hai? 10 second!”
Team A sochti reh gayi. Ananya ne turant likha: “25 hatao: 42. 42 = 6 × 7. To number 65!”
Agla sawaal: “36² = ?” Ananya ka haath ruka: “36 to 5 pe khatam nahi… dhokha! Seedha karna padega.” 1296. Sahi!
CharuMam (audience mein): “Dekha? Trick jaanna aadhi jeet hai. Kab nahi lagani, yeh jaanna poori jeet!” 🧠
— 📌 charumam.com
🪄 Trick Step by Step: Type Pehchano, Shart Check, Trick, Check
💡 Is post ki ek badi baat: Tricky sawaal mein pehle type pehchano (square 5 pe khatam? 3-digit? bahan-trick? ulta?). Phir shart check karo. Shart poori to trick, warna seedha tareeka. Aakhir mein andaaza ya seedhe tareeke se check.
Step 1: Type pehchano
5 pe khatam ka square (6.1, 6.2)? Dahai same + ikai jod 10 (6.3)? Square diya hai, number dhoondhna hai (ulta)? Pattern / farq?
Step 2: Shart check
Square trick: number 5 pe khatam. Bahan-trick: dahai same aur ikai jod 10. Shart toote to seedha tareeka.
Step 3: Trick lagao
× agla, peeche 25 (ya ikai × ikai, do digit mein). Ulta ho to: 25 hatao, “kaun × agla” dhoondo.
Step 4: Check
Andaaza (jaise 65² to 60 × 60 = 3600 se bada) ya seedha tareeka.
Yaad-patra
| Type | Example | Kya karo |
|---|---|---|
| 2-digit, 5 pe khatam | 65² | 6 × 7 = 42 → 4225 |
| 3-digit, 5 pe khatam | 125² | 12 × 13 = 156 → 15625 |
| Bahan-trick | 34 × 36 | 3 × 4 = 12, 4 × 6 = 24 → 1224 |
| Ulta | ? ka square 4225 | 25 hatao → 42 = 6 × 7 → 65 |
| Dhokha | 36², 45 × 55 | Shart nahi; seedha tareeka |
Ulta sawaal kaise? (Kis number ka square 4225?)
- Peeche ka 25 hatao: 42 bacha.
- 42 ko “kaun × agla” mein todo. Table dekho: 2, 6, 12, 20, 30, 42, 56, 72, 90 → 42 = 6 × 7.
- Chhota wala (6) lo aur peeche 5 lagao: 65.
- Check: 65²: 6 × 7 = 42 → 4225 ✅
Dhokha 1: 36²
36 pe aakhri digit 6 hai, 5 nahi. Bahan-trick bhi nahi (6 + 6 = 12). Seedha: 36 ko 30 baar = 1080 (360 ko 3 baar: 360, 720, 1080). 36 ko 6 baar = 216 (36, 72, 108, 144, 180, 216). Kul 1080 + 216 = 1296.
Dhokha 2: 45 × 55
Dono 5 pe khatam, par square nahi (do alag number), aur dahai alag (4 aur 5). Trick nahi! Seedha (Ch 5 ki madad se): 45 ko 50 baar = 4500 ka aadha = 2250. 45 ko 5 baar = 450 ka aadha = 225. Kul 2250 + 225 = 2475.
🆘 Atak gaye? Aise socho
- Ulta sawaal mein 42 kaun × agla? Table: 6 × 7 = 42. Phir chhota number + 5 = 65.
- Square jaisa dikhe? Pehle dekho: 5 pe khatam hai? Nahi to dhokha.
- Do alag number (45 × 55)? Bahan-trick ki shart (dahai same, ikai jod 10) check karo.
- Check: andaaza: 65² to 60 × 60 = 3600 aur 70 × 70 = 4900 ke beech hona chahiye. 4225 ✅
— 📌 charumam.com
🔍 Yeh Kaam Kyun Karta Hai?
Ulta kyun chalta hai? Seedha chalne pe 65² ka jawab: (6 × 7) aur peeche 25. To agar jawab 4225 hai, to aage ka hissa 42 hi “6 × 7” hai. Ek hi raasta, ulti disha mein.
Pattern kyun badhta hai? Neeche seedhi dekho: 2, 6, 12, 20, 30, 42, 56, 72, 90 (yeh “× agla” ke jawab hain). Har baar 4, 6, 8, 10 … zyada. Aage ka hissa saikde (100) mein hai, aur peeche ka 25 dono mein same rehta hai, isliye 4 saikde = 400. Isliye squares ka farq 400, 600, 800 … hota hai.
34 × 36 aur 35² ka rishta: 34 × 36 = 1224, 35² = 1225. Sirf 1 ka farq! Bahan-trick se: dono mein 3 × 4 = 12; peeche 4 × 6 = 24 aur 5 × 5 = 25. Isliye 1 kam.
— 📌 charumam.com
✏️ Solved Examples (Har Ek Normal Tareeke Se Check)
Example 1: 45² + 55² = ?
2025 + 3025 = 5050.
✔️ Normal tareeke se check: Seedha: 1800 + 225 = 2025 aur 2750 + 275 = 3025 (Before Timer). 2025 + 3025 = 5050 ✅
Example 2: Kis number ka square 4225 hai?
25 hatao: 42 = 6 × 7. Number 65.
✔️ Normal tareeke se check: Seedha: 65 ko 60 baar = 650 ko 6 baar: 650, 1300, 1950, 2600, 3250, 3900. 65 ko 5 baar = 325. Kul 3900 + 325 = 4225 ✅
Example 3: 34 × 36 = ?
Dahai same (3), 4 + 6 = 10 ✅. 3 × 4 = 12, 4 × 6 = 24 → 1224. (35² = 1225 se 1 kam!)
✔️ Normal tareeke se check: Seedha: 34 ko 30 baar = 1020 (340 ko 3 baar: 340, 680, 1020). 34 ko 6 baar = 204. Kul 1020 + 204 = 1224 ✅
Example 4: 36² = ? (dhokha!)
5 pe khatam nahi, bahan-trick bhi nahi. Seedha: 1080 + 216 = 1296.
✔️ Normal tareeke se check: Doosra tareeka: 36 ko 40 baar se 4 baar kam. 36 ko 40 baar = 1440 (360 ko 4 baar). 36 ko 4 baar = 144. 1440 − 144 = 1296 ✅
— 📌 charumam.com
🕉️ Vedic Maths Connection
Is chapter ki teeno tricks Vedic Maths ki kitabon mein “Ekadhikena Purvena” (pichle se ek zyada) wali soch se judti hain. Ulta sawaal (square se number) aage square root ke chapter (Ch 14) ki neev hai: square root matlab “kis number ka square yeh hai?”
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Trick use karein? | Kyun |
|---|---|---|
| Square, number 5 pe khatam | ✅ Haan | × agla, peeche 25. |
| Ulta: square 25 pe khatam, number dhoondo | ✅ Haan | 25 hatao, kaun × agla. |
| Dahai same, ikai jod 10 | ✅ Bahan-trick | Dahai × agla | ikai × ikai. |
| 36², 44² (5 pe khatam nahi) | ❌ Nahi | Seedha tareeka (tukdon mein). |
| 45 × 55 (dahai alag) | ❌ Nahi | Seedha; Ch 5 ka × 50 madad karega. |
| Teacher ne steps maange | ❌ Answer sheet pe nahi | Sheet pe seedha, rough mein trick. |
— 📌 charumam.com
❌→✅ Common Mistakes
Galti 1: Dhokha pe trick
Sawaal: 36²
❌ Galat: “3 × 4 = 12, peeche 25 → 1225.” (Yeh to 35² hai!)
✅ Sahi: 36 pe 5 nahi; seedha: 1296.
Galti 2: 45 × 55 pe bahan-trick
Sawaal: 45 × 55
❌ Galat: 4 × 5 = 20, 5 × 5 = 25 → 2025.
✅ Sahi: dahai alag (4, 5); shart nahi. Seedha: 2250 + 225 = 2475.
Galti 3: Ulte mein bada number liya
Sawaal: kis number ka square 4225?
❌ Galat: 42 = 6 × 7, to “75”.
✅ Sahi: chhota wala (6) lo: 65. (75² = 5625.)
Galti 4: Ulte mein 25 nahi hataya
Sawaal: kis number ka square 3025?
❌ Galat: 25 nahi hataya, aur 3025 ke pehle do digit 30 ki jagah 302 ko “kaun × agla” mein todne lage. 17 × 18 = 306, 16 × 17 = 272; 302 kisi “kaun × agla” mein theek nahi baithta, to bachcha atak gaya.
✅ Sahi: 25 hatao → 30 = 5 × 6 → 55.
🧠 Rule of thumb: Type → shart → trick → check. Shart na ho to trick nahi. Ulta: 25 hatao, chhota × agla dhoondo, peeche 5.
— 📌 charumam.com
🏃 Speed Drill: 15 Sawaal, Timer Ke Saath
15 mix sawaal: squares, bahan-trick, ulte sawaal aur 3 dhokhe. Pehle type dekho! Target: 6 minute.
- 25² = ?
- 65² = ?
- 95² = ?
- 105² = ?
- 155² = ?
- 34 × 36 = ?
- 52 × 58 = ?
- 71 × 79 = ?
- 113 × 117 = ?
- Kis number ka square 3025 hai?
- Kis number ka square 13225 hai?
- 35² − 25² = ?
- 45² + 55² = ?
- 36² = ?
- 45 × 55 = ?
Mera time: ______ · Sahi: ____ / 15
Answers dekho (pehle khud karo!)
- 625
- 4225
- 9025
- 11025
- 24025
- 1224
- 3016
- 5609
- 13221
- 55
- 115
- 600
- 5050
- 1296
- 2475
Kaise kiya (kuch): 113 × 117: aage 11 same, 3 + 7 = 10 ✅: 11 × 12 = 132, 3 × 7 = 21 → 13221. 13225: 25 hatao → 132 = 11 × 12 → 115. 35² − 25²: 1225 − 625 = 600.
— 📌 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.
- 15² = ?
- 45² = ?
- 75² = ?
- 85² = ?
- 125² = ?
- 44 × 46 = ?
- 63 × 67 = ?
- 92 × 98 = ?
- 21 × 29 = ?
- 35 × 35 = ?
| Rating | Kitne sahi, kitne time mein |
|---|---|
| 🌱 Beginner | 60 second mein 5 se 7 sahi. Badhiya shuruaat! |
| 🚀 Pro | 60 second mein 8 ya 9 sahi |
| 🏆 Champion | 10 mein 10 sahi, 60 second ke andar |
Answers dekho
- 225
- 2025
- 5625
- 7225
- 15625
- 2024
- 4221
- 9016
- 609
- 1225
5 se kam sahi? Koi baat nahi! Trick wala section ek baar aur padho aur kal phir try karo. Har din thoda better, bas yahi chahiye. 💪
— 📌 charumam.com
📝 10 MCQs (Har Option Ka Kaaran)
MCQ matlab ek sawaal ke chaar jawab (options) diye hote hain, unme se ek sahi chunna hai.
Q1. Kis number ka square 4225 hai?
Jawab aur kaaran dekho
Sahi jawab: (d) 65
- (a) galat ❌: 75² = 5625; 42 ka bada hissa (7) le liya.
- (b) galat ❌: 42 sirf aage ka hissa hai, number nahi.
- (c) galat ❌: 64 pe 5 nahi; 64² = 4096.
- (d) sahi ✅: 25 hatao: 42 = 6 × 7; chhota 6, peeche 5 → 65.
Q2. 36² = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 1296
- (a) galat ❌: 1236 mein 216 ki jagah 156 jod diya.
- (b) galat ❌: 936 bahut chhota; 36² to 30 × 30 = 900 se kaafi bada.
- (c) sahi ✅: Seedha: 1080 + 216 = 1296.
- (d) galat ❌: 1225 to 35² hai; 36 pe trick nahi lagti.
Q3. 45 × 55 = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 2475
- (a) galat ❌: 2525 andaaza galat hai; sahi hisaab 2250 + 225 = 2475.
- (b) sahi ✅: Seedha: 45 ko 50 baar = 2250, 5 baar = 225; kul 2475.
- (c) galat ❌: 2025 = 45², yahan 45 × 55 hai; bahan-trick ki shart nahi.
- (d) galat ❌: 3025 = 55².
Q4. 34 × 36 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 1224
- (a) sahi ✅: 3 × 4 = 12, 4 × 6 = 24 → 1224.
- (b) galat ❌: 1225 = 35²; 34 × 36 usse 1 kam.
- (c) galat ❌: 924 mein aage 3 × 4 ki jagah 3 × 3 = 9 kar diya; 9 ke peeche 24 = 924.
- (d) galat ❌: 1296 = 36².
Q5. 35² − 25² = ?
Jawab aur kaaran dekho
Sahi jawab: (d) 600
- (a) galat ❌: 35 − 25 = 10, aur 10² = 100; par squares ka farq aise nahi nikalta.
- (b) galat ❌: 400 = 25² − 15².
- (c) galat ❌: 10 to 35 − 25 hai.
- (d) sahi ✅: 1225 − 625 = 600.
Q6. Kaunse sawaal pe square-ending-5 trick NAHI lagegi?
Jawab aur kaaran dekho
Sahi jawab: (c) 44²
- (a) galat ❌: 105 pe 5: 11025.
- (b) galat ❌: 85 pe 5: 7225.
- (c) sahi ✅: 44 pe aakhri digit 4: trick nahi.
- (d) galat ❌: 45 pe 5: 2025.
Q7. Kis number ka square 13225 hai?
Jawab aur kaaran dekho
Sahi jawab: (b) 115
- (a) galat ❌: 105² = 11025.
- (b) sahi ✅: 25 hatao: 132 = 11 × 12 → 115.
- (c) galat ❌: 125² = 15625.
- (d) galat ❌: 132 aage ka hissa hai, number nahi.
Q8. Pattern: 15², 25², 35², 45² ke jawabon ka farq kaise badhta hai?
Jawab aur kaaran dekho
Sahi jawab: (a) 400, 600, 800 (har baar 200 zyada)
- (a) sahi ✅: 225, 625, 1225, 2025: farq 400, 600, 800.
- (b) galat ❌: 100 nahi; pehla farq hi 400 hai.
- (c) galat ❌: Barabar nahi; har baar badhta hai.
- (d) galat ❌: Double nahi: 400 se 600 double nahi hai.
Q9. Ek chaukor park ki bhuja 85 m hai. Area?
Jawab aur kaaran dekho
Sahi jawab: (d) 7225 varg metre
- (a) galat ❌: 340 = 85 × 4 (chaaron bhujaon ka jod, yaani ghera), area nahi.
- (b) galat ❌: 170 = 85 × 2, area nahi.
- (c) galat ❌: 7285 mein 25 ki jagah 85 likh diya.
- (d) sahi ✅: Area = 85 × 85: 8 × 9 = 72 → 7225.
Q10. 113 × 117 = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 13221
- (a) galat ❌: 12121 mein 11 × 11 kiya.
- (b) galat ❌: 13321 mein 132 ki jagah 133 likha.
- (c) sahi ✅: Aage 11 same, 3 + 7 = 10: 11 × 12 = 132, 3 × 7 = 21 → 13221.
- (d) galat ❌: 13225 = 115²; yahan ikai guna 21 hai, 25 nahi.
— 📌 charumam.com
🧠 Challenge: HOTS Aur Olympiad Style
HOTS matlab Higher Order Thinking Skills, yaani aise sawaal jinme sirf trick nahi, thoda dimaag bhi lagana padta hai. Olympiad ek maths competition (pratiyogita) hota hai.
Q1. 35² = 1225 pata hai. Bina poora guna kiye 36² nikaalo.
Solution dekho
Tiles socho: 35 × 35 ka chaukor. 36 × 36 banane ke liye ek nayi line (35 tile) neeche aur ek naya column (36 tile) side mein lagao. To 36² = 1225 + 35 + 36 = 1296.
Check: seedha 1080 + 216 = 1296 ✅
Q2. Do lagataar (ek ke baad agla, jaise 35 phir 45) 5 pe khatam numbers ke squares ka farq 1000 hai. Woh kaun?
Solution dekho
Seedhi (chitra) ka farq: 225 → 625 (400), 625 → 1225 (600), 1225 → 2025 (800), 2025 → 3025 (1000) ✅. To 45 aur 55.
Check: 3025 − 2025 = 1000 ✅
Q3. Raju ne 45 × 55 pe bahan-trick lagaya aur 2025 likha. Sahi ya galat? Kyun?
Solution dekho
Galat. Bahan-trick ki shart: dahai same aur ikai jod 10. Yahan dahai 4 aur 5 (alag), aur ikai 5 + 5 = 10 to hai, par pehli shart toot gayi. Sahi jawab seedha: 2250 + 225 = 2475.
Check: 2475 − 2025 = 450 ka farq, to Raju ka jawab bahut door tha.
Q4. Ek chaukor ki bhuja 25 m se badh kar 35 m ho gayi. Area kitna badha?
Solution dekho
Pehle: 25² = 625 varg metre. Baad: 35² = 1225 varg metre. Badha: 1225 − 625 = 600 varg metre.
Check: 625 + 600 = 1225 ✅
— 📌 charumam.com
🎯 Exam Mein Kahan Kaam Aayega?
| Exam | Kahan kaam aayega |
|---|---|
| School exam (Class 6–8) | Squares (number × wahi number) chapter: ulte sawaal, area (bhuja × bhuja). |
| Maths Olympiad | Pattern (farq 400, 600, 800 …), 36² = 35² + 35 + 36 jaisi soch. |
| NTSE / MAT | Numbers ki line (jaise 225, 625, 1225 …) mein squares pehchaanna. |
| SSC / Bank (aage) | Simplification mein squares aur unke farq. |
Shabdon ka matlab: Olympiad = school ke bachchon ki maths pratiyogita (competition). NTSE = Class 10 ke bachchon ka ek national scholarship (vazifa) exam. MAT = Mental Ability Test, yaani sochne-samajhne ki pariksha (NTSE ka ek hissa). SSC / Bank exam = badon ke sarkari naukri ke exam. Simplification = lambe hisaab ko chhota karke jawab nikaalna. Class 6–8 = school ki chhathi se aathvi kaksha.
— 📌 charumam.com
👩🏫 CharuMam Ka Tip
Har tricky sawaal pe khud se bolo: “Type? Shart? Trick? Check?” Yeh chaar shabd aapko har dhokhe se bachaayenge. Chapter 6 complete, aap champion ho! 🧠🏆
— 📌 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)
45²: 4 × 5 = 20 → 2025. 55²: 5 × 6 = 30 → 3025. Jodo: 2025 + 3025 = 5050 ✅
| 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 din ki practice chahiye. Phir yeh purane tareeke 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 galti hone pe samjhayega:
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❓ FAQs (Bachchon Ke Asli Sawaal)
1. Chapter 6 khatam ho gaya?
Haan! Chapter 6 ke page pe saare 4 posts ek jagah milenge.
2. Ulta sawaal har square pe chalega?
Sirf un squares pe jo 25 pe khatam hon (yaani 5 pe khatam number ke square). 1296 jaise pe nahi.
3. 36² ki bhi koi trick hai?
Haan, aage Chapter 13 (Fast Squaring Near Base) mein. Abhi seedha tareeka, ya 35² + 35 + 36 (Challenge).
4. Agla chapter kya hai?
Level 2 shuru: Ch 7 “Near 10/100: Base Method”, jald aa raha hai!
— 📌 charumam.com
🟢 Recap: Aaj Kya Seekha
- Pehle type aur shart, phir trick, phir check.
- Ulta: 25 hatao, kaun × agla, chhota + 5 (4225 → 65).
- Pattern: squares ka farq 400, 600, 800 …
- 34 × 36 = 1224, 35² = 1225 (1 ka farq).
- Dhokhe: 36² = 1296, 45 × 55 = 2475 (trick nahi).
- Area: chaukor = bhuja × bhuja.
— charumam.com 🎯
👉 Aage Kya?
Chapter 6 complete! 🎉 Level 1 poora hua. Ab Level 2: Multiplication Magic, Ch 7 jald aa raha hai.
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
- ▶️ YouTube (subscribe): @charumamofficial
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