Viral Maths — Ch07: Square Roots

📌 What This Chapter Covers

Square Roots chapter is short but powerful — sirf 2 named techniques hain, dono "Guess Approach" family ke.
Prerequisite: squares 1–100 poori tarah yaad hone chahiye (Ch01 Important Products se) — bina iske yeh approaches slow ho jaate hain.
Technique 1 general 4-digit perfect squares ke liye, Technique 2 specifically numbers ending in 25 ke liye (fastest).

⚡ QUICK RECALL

Perfect squares sirf 0, 1, 4, 5, 6, 9 pe end hote hain — kabhi 2, 3, 7, 8 pe nahi. Yeh fact answer verify karne mein kaam aata hai.

🗂️ Chapter Index

Tab	Technique	Best For
2	Guess Approach (General)	Any 4-digit perfect square
3	Ending in 25 (Guess Approach)	Perfect squares ending in 25 (fastest method)
4	Master Table	Both techniques summarized

Square Root of Any Number — Guess Approach

Example: √7921

Step 1: Find nearby squares: 85² = 7225 Step 2: Next: 90² = 8100 Step 3: 7921 lies between 7225 and 8100, so root lies between 85 and 90 Step 4: Units digit of 7921 is 1 → the root must end in a digit that gives 1 when squared Step 5: Only 9² ends in 1 → Answer = 89

⚡ QUICK RECALL — Units Digit Mapping

Square ends in 1 → root ends in 1 or 9 Square ends in 4 → root ends in 2 or 8 Square ends in 9 → root ends in 3 or 7 Square ends in 6 → root ends in 4 or 6 Square ends in 5 → root ends in 5 Square ends in 0 → root ends in 0

⚠ EXAM TRAP

Ek units digit se do possible answers aa sakte hain (jaise 1 → 1 ya 9) — tabhi Step 1-3 ka range-bounding zaroori hai taaki sahi wala choose kar sako.

Square Root of Number Ending with 25 — Guess Approach

Example: √5625

Step 1: Break the number leaving 2 digits from the right: 56 | 25 Step 2: Square root of 25 (fixed) = 5 Step 3: Find factors of 56 whose difference is 1: 7×8 = 56 Step 4: Take the SMALLER factor: 7 Step 5: Combine: root = 75

⚡ QUICK RECALL

Numbers ending in 25 ka square root hamesha khud bhi 5 pe end hota hai. Left part ko do consecutive numbers ke product ke roop mein todo, smaller factor lo.

⚠ EXAM TRAP

Hamesha SMALLER factor lena hai, bigger nahi — 56=7×8 mein 7 sahi answer deta hai (75²=5625 ✓), 8 nahi.

📋 Master Table — Square Root Techniques

Technique	Applies To	Core Method
Guess Approach (General)	Any 4-digit perfect square	Bound between two known squares, match units digit
Ending in 25	Perfect squares ending in 25	Right part always →5; left part → consecutive-factor pair, take smaller

🔑 Units Digit Reference (for General Approach)

Perfect Square Ends In	Root Ends In
0	0
1	1 or 9
4	2 or 8
5	5
6	4 or 6
9	3 or 7

⚡ QUICK RECALL

Perfect squares KABHI 2, 3, 7, 8 pe end nahi hote — agar exam mein ऐसा number dikhe, wo perfect square nahi hai.