Mathematics Short Tricks/SQUARE TRICKS AND SQUARE ROOT TRICKS IN MATHEMATICS.
Mathematics Short Tricks/SQUARE TRICKS AND SQUARE ROOT TRICKS IN MATHEMATICS.
Contents
- 1 Mathematics Short Tricks – Square & Square Root Tricks
- 2 Square Tricks (तेजी से वर्ग निकालने की ट्रिक्स)
- 3 Any Number Ending in 5
- 4 Square of Numbers Near 50
- 5 Square of Numbers Close to 100
- 6 Square Root Tricks (तेजी से वर्गमूल निकालने की ट्रिक्स)
- 7 Perfect Squares Identification
- 8 Square Root of Perfect Squares (Quick Trick)
- 9 Estimating Square Roots of Non-Perfect Squares
- 10 Final Tips for Quick Calculation
- 11 Mathematics Short Tricks/SQUARE TRICKS AND SQUARE ROOT TRICKS IN MATHEMATICS.
- 12 Vedic Mathematics Tricks and Shortcuts
- 13 Squares and Square Roots
Mathematics Short Tricks – Square & Square Root Tricks
Learning square and square root tricks helps in fast calculations, which is useful for competitive exams like SSC, Banking, GATE, and more. Below are some powerful tricks to speed up your calculations.
Square Tricks (तेजी से वर्ग निकालने की ट्रिक्स)
Any Number Ending in 5
For numbers ending in 5, use this simple trick:
Formula:
(AB)2=A×(A+1)और अंत में 25 जोड़ दें।(AB)^2 = A \times (A+1) \quad \text{और अंत में 25 जोड़ दें।}
Example: 35235^2
- Take first digit (3) → Multiply by next number → 3×4=123 \times 4 = 12
- Add 25 at the end → 1225
Answer: 352=122535^2 = 1225
Example: 75275^2
- 7×8=567 \times 8 = 56, add 25 → 5625
Answer: 752=562575^2 = 5625
Square of Numbers Near 50
For numbers close to 50 (50±x50 \pm x), use:
Formula:
N2=25+x∣x2N^2 = 25 + x \quad | \quad x^2
Example: 48248^2
- x=50−48=2x = 50 – 48 = 2
- 25−2=2325 – 2 = 23 | 22=042^2 = 04
- Answer: 2304
Example: 52252^2
- x=52−50=2x = 52 – 50 = 2
- 25+2=2725 + 2 = 27 | 22=042^2 = 04
- Answer: 2704
Square of Numbers Close to 100
For numbers close to 100 (100±x100 \pm x), use:
Formula:
N2=(100+x)×(100+x)=(100+2x)∣x2N^2 = (100 + x) \times (100 + x) = (100 + 2x) | x^2
Example: 96296^2
- 100−96=4100 – 96 = 4, so
- (96+4)=96+4=92(96 + 4) = 96 + 4 = 92 | 42=164^2 = 16
- Answer: 9216
Example: 1042104^2
- 104+4=108104 + 4 = 108 | 42=164^2 = 16
- Answer: 10816
Square Root Tricks (तेजी से वर्गमूल निकालने की ट्रिक्स)
Perfect Squares Identification
If a number ends in 2, 3, 7, 8, it cannot be a perfect square.
Example: 743743 → Ends in 3 → Not a perfect square
Example: 441441 → Ends in 1 → Perfect square (21221^2)
Square Root of Perfect Squares (Quick Trick)
For perfect squares, break the number into two parts and identify the nearest square root.
Example: 4489\sqrt{4489}
- First two digits → 44 (Nearest square = 62^2 = 36, 72^2 = 49)
- Last digit → 9 (So the unit place is 3 or 7)
- Check: 672=448967^2 = 4489
Answer: 67
Estimating Square Roots of Non-Perfect Squares
Find the nearest perfect squares and use approximation.
Example: 50\sqrt{50}
- Nearest squares: 49(72)49 (7^2) and 64(82)64 (8^2)
- Since 50 is closer to 49, √50 ≈ 7.07
Final Tips for Quick Calculation
Memorize squares of 1 to 30
Use approximation tricks for non-perfect squares
Practice breaking numbers into smaller calculations
With these tricks, you’ll solve squares and square roots in seconds!
