35 × 35 kitna? Lamba guna lagta hai, par jo number 5 pe khatam ho, uska square sirf do chhote step mein: aakhri 5 hatao, jo bacha use uske agle number se guna karo, aur peeche 25 likh do. Pehle samjhenge square (²) kya hai, phir trick, phir chitra se kyun. Chapter 6 shuru!
⏱ Before Timer: Pehle Purane Tareeke Se
Pehle seedha tareeka. 35 × 35 matlab 35 ko 35 baar jodna. 35 = 30 + 5, to 35 ko 30 baar, aur 35 ko 5 baar, phir dono jodo (GUNA box wali tukdon ki soch):
- 35 ko 10 baar = 350 (peeche 0). 30 baar = 10 baar, teen baar: 350, 700, 1050. To 35 ko 30 baar = 1050.
- 35 ko 5 baar = 350 ka aadha (Post 5.1: × 5 = peeche 0, phir aadha). 350 = 300 + 50 → 150 + 25 = 175.
- Dono jodo: 1050 + 175 = 1225.
Kaafi steps! Trick mein bas 3 × 4 aur 25.
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
35 × 35 = 1225
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 teen cheezein chahiye: square (²) ka matlab, ek number × uska agla number (jaise 3 × 4), aur 100 se guna (peeche 00, Chapter 5). Sab neeche ke boxes mein hai. Naye shabd:
📖 Shabd jo is post mein aayenge
- Square (varg), nishaan ²: number ko usi number se guna. 35² = 35 × 35. Dhyaan: 35² ka matlab 35 × 2 nahi!
- 5 pe khatam number: jiska aakhri (ikai) digit 5 ho: 15, 25, 35, … 95.
- Aakhri 5 hatao: number se ikai wala 5 hata do; jo bache woh lo. 35 → 3. 85 → 8.
- Agla number: theek baad wala number (+ 1). 3 ka agla 4, 8 ka agla 9, 9 ka agla 10.
- Peeche 25 likhna: guna ke jawab ke right mein 25 likh dena: 12 → 1225. Place value mein: 12 saikde + 25, yaani 1200 + 25.
- Tile / dabba: chhota chaukor tukda. 35 × 35 ko 35 line, har line mein 35 tile ka chaukor socho.
📏 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.
🔟 10 se guna = peeche ek 0 lagao
GUNA box mein dekha: 3 × 10 matlab 10 ko 3 baar jodo: 10 + 10 + 10 = 30. Isi tarah 46 × 10 matlab 46 ko 10 baar jodna. 46 mein 4 dahai aur 6 ikai hain. 10 baar lene pe 6 ikai ban jaati hain 6 dahai (60), aur 4 dahai ban jaati hain 4 saikde (400). Kul 400 + 60 = 460.
Aasaan niyam: kisi poore number ko 10 se guna karna ho to uske peeche (right mein) ek 0 likh do. Har digit ek jagah left khisak jaata hai, aur ikai ki khaali jagah mein 0 aa jaata hai.
| Number | × 10 | Kya hua |
|---|---|---|
| 7 | 70 | 7 ikai → 7 dahai |
| 46 | 460 | 4 dahai → 4 saikde, 6 ikai → 6 dahai |
| 128 | 1280 | har digit ek jagah left, peeche 0 |
| 365 | 3650 | har digit ek jagah left, peeche 0 |
💯 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.
🔁 Chhota sa warm-up
- 3 × 4 = ?
- 12 × 100 = ?
- 1200 + 25 = ?
Answers dekho
- 12
- 1200 (peeche 00)
- 1225
Teeno aa gaye? Yahi milkar 35² = 1225 ban jaata hai!
— 📌 charumam.com
🎬 Kahani: Kabir Ka Chaukor Bagicha
Kabir ke dada ji ka bagicha (garden) ek chaukor tha: 35 qadam lamba, 35 qadam chauda. Unhone poocha: “Agar har 1 qadam × 1 qadam pe ek tile lagaayein, to kitni tile chahiye?”
Kabir: “35 × 35… 35 ko 35 baar jodna padega!” 😟
Didi muskurayi: “3 aur uska agla 4. 3 × 4 = 12. Peeche 25. 1225 tile!” Kabir ne seedhe tareeke se karke dekha: 1050 + 175 = 1225. “Arre! Sahi hai!”
CharuMam: “Aaj yahi seekhenge, aur chitra se dekhenge ki yeh kyun hamesha sahi aata hai.” 🟦
— 📌 charumam.com
🪄 Trick Step by Step: Aakhri 5 Hatao, Agle Se Guna, Peeche 25
💡 Is post ki ek badi baat: Jo number 5 pe khatam ho, uska square = (aakhri 5 hatane pe jo bacha) × (uska agla number), aur uske peeche 25. 35²: 3 × 4 = 12, peeche 25 → 1225.
Step 1: Pakka karo: number 5 pe khatam hai
Sawaal: 35² (yaani 35 × 35). Aakhri digit 5 hai ✅. Trick lagegi.
Step 2: Aakhri 5 hatao
35 se 5 hatao: 3 bacha.
Step 3: Usko agle number se guna karo
3 ka agla number 4 (3 + 1 = 4). 3 × 4 = 12 (4 + 4 + 4 = 12).
Step 4: Peeche 25 likho
12 ke peeche 25: 1225. Matlab 12 saikde + 25 = 1200 + 25 = 1225. To 35² = 1225.
Saare 2-digit (15 se 95)
| Square | Aakhri 5 hatao | × agla | Peeche 25 |
|---|---|---|---|
| 15² | 1 | 1 × 2 = 2 | 225 |
| 25² | 2 | 2 × 3 = 6 | 625 |
| 35² | 3 | 3 × 4 = 12 | 1225 |
| 45² | 4 | 4 × 5 = 20 | 2025 |
| 55² | 5 | 5 × 6 = 30 | 3025 |
| 65² | 6 | 6 × 7 = 42 | 4225 |
| 75² | 7 | 7 × 8 = 56 | 5625 |
| 85² | 8 | 8 × 9 = 72 | 7225 |
| 95² | 9 | 9 × 10 = 90 | 9025 |
25 peeche kyun likhte hain? (Place value)
Jawab do hisson ka hai: 12 saikde (yaani 12 × 100 = 1200) aur 25. 1200 + 25 jodo: 1200 ki ikai aur dahai mein 0 0 hain, aur 25 ke 2 dahai aur 5 ikai seedhe un khaali jagahon mein baith jaate hain (Place box niyam). To 1200 + 25 = 1225. Isliye “12 ke peeche 25 likhna” aur “1200 + 25” ek hi baat hai.
95² mein dhyaan: 9 × 10 = 90. 90 ke peeche 25: 9025 (9000 + 25). 90 ka 0 mat chhodo! 925 galat hai.
15² mein: 1 × 2 = 2. 2 ke peeche 25: 225 (200 + 25).
🆘 Atak gaye? Aise socho
- Agla number kaunsa? Bas 1 jodo: 3 → 4, 7 → 8, 9 → 10.
- × agla yaad nahi? Upar ki table (“Number × agla number”) dekho, ya baar-baar jodo: 7 × 8 matlab 8 ko 7 baar.
- Jawab mein kitne digit? 2-digit number ka square 3 ya 4 digit ka hota hai (15² = 225, 95² = 9025). Aakhri do digit hamesha 25.
- Check: seedha tareeka: 35 ko 30 baar + 35 ko 5 baar = 1050 + 175 = 1225.
— 📌 charumam.com
🔍 Yeh Kaam Kyun Karta Hai?
Square ko tiles ka chaukor socho: 35 × 35 matlab 35 line, har line mein 35 tile. Ab is chaukor ko 4 hisson mein kaato (chitra ka baayan hissa):
- Neela bada chaukor: 30 × 30
- Daayein patli naarangi patti B: 30 lambi, 5 chaudi (5 × 30)
- Neeche patli hari patti C: 30 × 5
- Kone mein chhota gulaabi chaukor D: 5 × 5 = 25
Ab naarangi patti B ko utha kar, ghuma kar, hari patti ke neeche laga do (chitra ka daayan hissa). Tile wahi hain, bas jagah badli. Neela + hara + naarangi milkar ek lamba aayat (rectangle) ban gaya: chaudai 30, lambai 30 + 5 + 5 = 40.
Is aayat mein tile: 30 × 40. 30 ko 4 baar = 120, aur 40 = 4 ka 10 guna, to 120 ka 10 guna = 1200. (Chhota raasta: 3 × 4 = 12, aur dono ke 0 milakar peeche 00.) Upar se gulaabi kona D: 5 × 5 = 25. Kul tile: 1200 + 25 = 1225.
Dekha? “3 × 4” mein 4 isliye aaya kyunki patti hilane se 30 wali lambai 40 ban gayi (agla dahai). Aur 25 woh chhota kona hai jo hamesha 5 × 5 hi hota hai!
— 📌 charumam.com
✏️ Solved Examples (Har Ek Normal Tareeke Se Check)
Example 1: 45² = ?
Aakhri 5 hatao: 4. Agla 5. 4 × 5 = 20. Peeche 25: 2025.
✔️ Normal tareeke se check: Seedha: 45 ko 40 baar + 45 ko 5 baar. 45 ko 10 baar = 450; 40 baar = 450 ko 4 baar: 450, 900, 1350, 1800. 45 ko 5 baar = 450 ka aadha = 225. Kul 1800 + 225 = 2025 ✅
Example 2: 65² = ?
6 × 7 = 42. Peeche 25: 4225.
✔️ Normal tareeke se check: Seedha: 65 ko 60 baar = 650 ko 6 baar: 650, 1300, 1950, 2600, 3250, 3900. 65 ko 5 baar = 650 ka aadha = 325. Kul 3900 + 325 = 4225 ✅
Example 3: 85² = ?
8 × 9 = 72. Peeche 25: 7225.
✔️ Normal tareeke se check: Seedha: 85 ko 80 baar = 850 ko 8 baar: 850, 1700, 2550, 3400, 4250, 5100, 5950, 6800. 85 ko 5 baar = 425. Kul 6800 + 425 = 7225 ✅
Example 4: 25² = ?
2 × 3 = 6. Peeche 25: 625.
✔️ Normal tareeke se check: Chapter 5 se: 25 × 25 = peeche 00, aadha, aadha: 2500 → 1250 → 625 ✅
— 📌 charumam.com
🕉️ Vedic Maths Connection
Vedic Maths ki kitabon mein is trick ko “Ekadhikena Purvena” sutra se joda jaata hai. Iska rough matlab hai “pichle wale se ek zyada”, yaani agla number. 35² mein 3 ko uske “ek zyada” (4) se guna karte hain. Hum naam se zyada chitra wali wajah yaad rakhenge.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Trick use karein? | Kyun |
|---|---|---|
| 2-digit number jo 5 pe khatam (15 se 95) | ✅ Haan | Do second: × agla, peeche 25. |
| 3-digit jaise 105², 115² | ⚠️ Post 6.2 | Wahi trick, bas 10 × 11 jaise guna seekhne padenge. |
| Number 5 pe khatam nahi (36², 44²) | ❌ Nahi | Trick sirf 5 pe khatam numbers ke liye. |
| 35 × 45 (do alag number) | ❌ Nahi | Square nahi hai; dono number alag hain. |
| 43 × 47 jaisa | ⚠️ Post 6.3 | Bahan-trick: same dahai, ikaiyon ka jod 10 (Post 6.3 mein samjhenge). |
| Teacher ne steps maange | ❌ Answer sheet pe nahi | Sheet pe seedha tareeka, rough mein trick se check. |
— 📌 charumam.com
❌→✅ Common Mistakes
Galti 1: Agle ki jagah wahi number
Sawaal: 35²
❌ Galat: 3 × 3 = 9, peeche 25 → 925.
✅ Sahi: 3 × 4 = 12 → 1225. Andaaza: 35² to 30 × 30 = 900 se bada hona chahiye, 925 bahut kam hai.
Galti 2: 25 ki jagah sirf 5
Sawaal: 35²
❌ Galat: 12 ke peeche 5 → 125.
✅ Sahi: peeche poora 25 (5 × 5 = 25): 1225.
Galti 3: 95² mein 0 chhoot gaya
Sawaal: 95²
❌ Galat: 9 × 10 = 90, phir “925”.
✅ Sahi: 90 ke peeche 25 → 9025.
Galti 4: ² ko × 2 samjha
Sawaal: 35²
❌ Galat: 35 × 2 = 70.
✅ Sahi: 35² = 35 × 35 = 1225.
🧠 Rule of thumb: 5 pe khatam? Aakhri 5 hatao, × agla, peeche 25. ² matlab number × wahi number.
— 📌 charumam.com
🏃 Speed Drill: 15 Sawaal, Timer Ke Saath
Timer lagao. 15 sawaal: kuch ² wale, kuch × wale (dono same matlab). Target: 3 minute.
- 15² = ?
- 25² = ?
- 35² = ?
- 45² = ?
- 55² = ?
- 65² = ?
- 75² = ?
- 85² = ?
- 95² = ?
- 35 × 35 = ?
- 75 × 75 = ?
- 15 × 15 = ?
- 45 × 45 = ?
- 85 × 85 = ?
- 95 × 95 = ?
Mera time: ______ · Sahi: ____ / 15
Answers dekho (pehle khud karo!)
- 225
- 625
- 1225
- 2025
- 3025
- 4225
- 5625
- 7225
- 9025
- 1225
- 5625
- 225
- 2025
- 7225
- 9025
Kaise kiya (kuch): 75²: 7 × 8 = 56 → 5625. 95²: 9 × 10 = 90 → 9025. 15²: 1 × 2 = 2 → 225.
— 📌 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.
- 25² = ?
- 65² = ?
- 85² = ?
- 15² = ?
- 45² = ?
- 95² = ?
- 35² = ?
- 55² = ?
- 75² = ?
- 25² = ?
| 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
- 625
- 4225
- 7225
- 225
- 2025
- 9025
- 1225
- 3025
- 5625
- 625
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. 35² = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 1225
- (a) sahi ✅: 3 × 4 = 12, peeche 25: 1225.
- (b) galat ❌: 925 tab aata hai jab 3 × 3 kiya; agla number (4) lena tha.
- (c) galat ❌: 70 = 35 × 2; ² ka matlab × 2 nahi, × khud.
- (d) galat ❌: 1525 mein 3 × 5 = 15 kiya; agla number 4 hai, 5 nahi.
Q2. 35² ka matlab kya hai?
Jawab aur kaaran dekho
Sahi jawab: (d) 35 × 35
- (a) galat ❌: 35 × 2 = 70; yeh ² ka matlab nahi.
- (b) galat ❌: 35 + 35 = 70, jod hai, square nahi.
- (c) galat ❌: 35 + 2 = 37, bilkul alag.
- (d) sahi ✅: ² matlab number ko usi number se guna.
Q3. 85² mein pehla step (aakhri 5 hatane ke baad) kya hai?
Jawab aur kaaran dekho
Sahi jawab: (c) 8 × 9
- (a) galat ❌: 5 to hata diya tha; 8 × 5 galat.
- (b) galat ❌: Jod nahi, guna karna hai.
- (c) sahi ✅: 8 ko uske agle number 9 se guna: 72, phir 25 → 7225.
- (d) galat ❌: 8 × 8 mein agla number nahi liya.
Q4. 95² = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 9025
- (a) galat ❌: 9925 mein 90 ki jagah 99 likh diya.
- (b) sahi ✅: 9 × 10 = 90, peeche 25: 9025.
- (c) galat ❌: 925 mein 90 ka 0 chhoot gaya.
- (d) galat ❌: 8125 tab jab 9 × 9 = 81 kiya; agla 10 lena tha.
Q5. Jawab ke peeche hamesha 25 kyun aata hai?
Jawab aur kaaran dekho
Sahi jawab: (a) Kyunki kone wala chhota chaukor 5 × 5 = 25 hai
- (a) sahi ✅: Chitra mein 5 × 5 ka kona hamesha bachta hai: 25 tile.
- (b) galat ❌: 25 sabse chhota number nahi hai; wajah kone ka 5 × 5 hai.
- (c) galat ❌: Har number mein 2 nahi hota (jaise 85).
- (d) galat ❌: 5 + 5 = 10 hota hai, 25 nahi; 25 = 5 × 5.
Q6. 15² = ?
Jawab aur kaaran dekho
Sahi jawab: (d) 225
- (a) galat ❌: 125 mein 1 × 1 kiya; agla 2 lena tha.
- (b) galat ❌: 25 sirf aakhri hissa hai; aage 2 bhi chahiye.
- (c) galat ❌: 215 mein 25 ki jagah 15 likha.
- (d) sahi ✅: 1 × 2 = 2, peeche 25: 225.
Q7. Kis sawaal pe yeh trick SEEDHI lagegi?
Jawab aur kaaran dekho
Sahi jawab: (c) 75²
- (a) galat ❌: 76 pe aakhri digit 6 hai, 5 nahi.
- (b) galat ❌: 75 × 85 square nahi: do alag number.
- (c) sahi ✅: 75 pe aakhri digit 5 hai, aur yeh square hai: 7 × 8 = 56 → 5625.
- (d) galat ❌: 74 pe aakhri digit 4 hai, 5 nahi.
Q8. 1225 mein “12” kya batata hai?
Jawab aur kaaran dekho
Sahi jawab: (b) 12 saikde, yaani 1200
- (a) galat ❌: 12 hazaar = 12000, bahut bada.
- (b) sahi ✅: 1225 = 1200 + 25; 12 saikde = 12 × 100.
- (c) galat ❌: Ikai mein sirf ek digit hota hai (5).
- (d) galat ❌: 12 dahai = 120 hota, par yahan 1200 hai.
Q9. 55² = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 3025
- (a) sahi ✅: 5 × 6 = 30, peeche 25: 3025.
- (b) galat ❌: 2525 mein 5 × 5 kiya; agla 6 lena tha.
- (c) galat ❌: 3055 mein 25 ki jagah 55 likh diya.
- (d) galat ❌: 325 mein 30 ka 0 chhoot gaya.
Q10. Chitra mein 35 × 35 ka chaukor kis ke barabar banta hai?
Jawab aur kaaran dekho
Sahi jawab: (d) 30 × 40 ka aayat + 5 × 5 ka kona
- (a) galat ❌: 30 × 30 = 900, aur dono pattiyaan bhi chahiye; sirf 5 jodna galat.
- (b) galat ❌: 35 × 2 = 70, bahut chhota.
- (c) galat ❌: 40 × 40 = 1600, bahut bada.
- (d) sahi ✅: Patti hilane se 30 × 40 = 1200, aur kona 25: kul 1225.
— 📌 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. Kis number ka square 5625 hai? (Number 5 pe khatam hai)
Solution dekho
Ulta chalo: peeche ka 25 hatao: 56 bacha. 56 = kaun × uska agla? 7 × 8 = 56 ✅. To aakhri 5 se pehle 7 tha: number 75.
Check: 75²: 7 × 8 = 56 → 5625 ✅
Q2. Ek chaukor park ki ek bhuja 45 metre hai. Uska kshetrafal (area) kitna?
Solution dekho
(Metre = lambai ka naap, lagbhag ek bada qadam. Kshetrafal / area = andar kitni 1 metre × 1 metre wali tile aayengi. Chaukor ka area = bhuja × bhuja.) 45 × 45 = 45²: 4 × 5 = 20 → 2025 varg metre (square metre).
Check: 1800 + 225 = 2025 ✅ (Example 1)
Q3. 35² aur 25² mein kitna farq hai?
Solution dekho
35² = 1225, 25² = 625. Farq: 1225 − 625 = 600. (1225 − 600 = 625 ✅)
Pattern: 15², 25², 35², 45²: 225, 625, 1225, 2025. Farq: 400, 600, 800. Har baar 200 zyada!
Q4. Kaunsa bada: 65² ya 4000 + 200?
Solution dekho
65²: 6 × 7 = 42 → 4225. 4000 + 200 = 4200. To 65² bada hai, 25 se.
Check: 4225 − 4200 = 25 ✅
— 📌 charumam.com
🎯 Exam Mein Kahan Kaam Aayega?
| Exam | Kahan kaam aayega |
|---|---|
| School exam (Class 6–8) | Squares (number × wahi number) wale chapter mein 15², 25², 35² jaldi chahiye; chaukor ka area (bhuja × bhuja). |
| Maths Olympiad | Pattern (225, 625, 1225 …) aur ulte sawaal: kis number ka square 5625? |
| NTSE / MAT | Numbers ki line (jaise 225, 625, 1225…) aur mental calculation mein squares. |
| SSC / Bank (aage) | Simplification mein 75², 85² jaise squares bahut aate hain. |
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. Mental calculation = bina copy-pencil ke, mann mein hisaab karna. Class 6–8 = school ki chhathi se aathvi kaksha.
— 📌 charumam.com
👩🏫 CharuMam Ka Tip
15² se 95² tak ki table ek baar zor se bolo: “ek-do do, do sau pachchees… nau-das nabbe, nau hazaar pachchees!” Teen din mein yaad ho jaayegi, aur Chapter 7 ke liye bhi kaam aayegi. 🟦
— 📌 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)
Aakhri 5 hatao: 3 bacha. 3 ka agla number 4. 3 × 4 = 12. Peeche 25: 1225 ✅
| 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:
— 📌 charumam.com
❓ FAQs (Bachchon Ke Asli Sawaal)
1. Kya yeh 3-digit numbers pe bhi chalti hai?
Haan! 105², 115² jaise. Agle Post 6.2 mein, jahan 10 × 11, 11 × 12 jaise guna pehle seekhenge.
2. Peeche 25 hi kyun, 5 kyun nahi?
Kyunki aakhri kona 5 × 5 = 25 hai, aur jawab = (… saikde) + 25. Isliye do digit: 2 aur 5.
3. 5² khud kya hai?
5² = 5 × 5 = 25. Trick se: aakhri 5 hatao, kuch nahi bacha (0). 0 × 1 = 0 (0 ko 1 baar jodo = 0), peeche 25 → 25. Wahi!
4. Agle post mein kya hai?
Post 6.2: yeh kyun chalta hai (aur pakka) + 105², 115², 125².
— 📌 charumam.com
🟢 Recap: Aaj Kya Seekha
- ² matlab number × wahi number: 35² = 35 × 35.
- 5 pe khatam: aakhri 5 hatao, × agla number, peeche 25.
- 35² → 3 × 4 = 12 → 1225.
- 25 isliye kyunki kona 5 × 5 = 25; 12 matlab 12 saikde (1200).
- 95² = 9025 (90 ka 0 mat chhodo).
- Check: seedha tareeka, jaise 1050 + 175 = 1225.
— charumam.com 🎯
👉 Aage Kya?
Ab 3-digit squares: Post 6.2 mein 105², 115², 125², pehle 10 × 11, 11 × 12 seekh kar, aur chitra se pakka “kyun”!
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬
💛 Post Achha Laga? Like, Share, Subscribe, Follow!
Agar aaj kuch naya samajh aaya, to post ko like kijiye, apne doston aur class ke group mein share kijiye, aur roz nayi trick ke liye humein subscribe aur follow kijiye! 🙏
- 🌐 Website: charumam.com
- 🤖 AI Tutor (doubt poochho, 24×7): tutor.charumam.com
- ▶️ YouTube (subscribe): @charumamofficial
- 📸 Instagram (follow): @charumamofficial
- ✈️ Telegram: t.me/charumam
- 💬 WhatsApp Channel: CharuMam WhatsApp Channel
— 📌 charumam.com
