√ Viral Maths — Chapter 07: Square Roots

by Navneet Tiwari (Adda247)  ·  2 Named Techniques for Finding Square Roots Fast · Bank / SSC / Railway / BPSC / BSSC

📌 What This Chapter Covers
  • The Square Roots chapter is short but powerful. It contains only two named techniques, both belonging to the Guess Approach family.
  • Prerequisite: the squares from 1 to 100 must be memorized completely from Chapter 1. Without them, these approaches become slow.
  • Technique 1 is for general four-digit perfect squares; Technique 2 is specifically for numbers ending in 25 and is the fastest.
⚡ QUICK RECALL
Perfect squares can end only in 0, 1, 4, 5, 6 or 9—never in 2, 3, 7 or 8. This fact helps verify an answer.
🗂️ Chapter Index
TabTechniqueBest For
2Guess Approach (General)Any 4-digit perfect square
3Ending in 25 (Guess Approach)Perfect squares ending in 25 (fastest method)
4Master TableBoth 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
A units digit may produce two possible answers, such as 1 → 1 or 9. Therefore, the range bounding in Steps 1–3 is essential for choosing the correct one.
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
The square root of a number ending in 25 always ends in 5. Express the left part as the product of two consecutive numbers and take the smaller factor.
⚠ EXAM TRAP
Always take the SMALLER factor, not the larger one. In 56=7×8, 7 gives the correct answer (75²=5625 ✓), not 8.
📋 Master Table — Square Root Techniques
TechniqueApplies ToCore Method
Guess Approach (General)Any 4-digit perfect squareBound between two known squares, match units digit
Ending in 25Perfect squares ending in 25Right part always →5; left part → consecutive-factor pair, take smaller
🔑 Units Digit Reference (for General Approach)
Perfect Square Ends InRoot Ends In
00
11 or 9
42 or 8
55
64 or 6
93 or 7
⚡ QUICK RECALL
Perfect squares NEVER end in 2, 3, 7 or 8. If such a number appears in an exam, it is not a perfect square.