Mathematics Short Tricks/SQUARE TRICKS AND SQUARE ROOT TRICKS IN MATHEMATICS.

Mathematics Short Tricks/SQUARE TRICKS AND SQUARE ROOT TRICKS IN MATHEMATICS.

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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।}(AB)2=A×(A+1)और अंत में 25 जोड़ दें।

Example: 35235^2352

• Take first digit (3) → Multiply by next number → $3\times 4=12$
• Add 25 at the end → 1225

Answer: 352=122535^2 = 1225352=1225

Example: 75275^2752

• $7\times 8=56$, add 25 → 5625

Answer: 752=562575^2 = 5625752=5625

 Square of Numbers Near 50

For numbers close to 50 ($50\pm x$), use:

Formula:

N2=25+x∣x2N^2 = 25 + x \quad | \quad x^2N2=25+x∣x2

Example: 48248^2482

• $x=50-48=2$
• $25-2=23$ | 22=042^2 = 0422=04
• Answer: 2304

Example: 52252^2522

• $x=52-50=2$
• $25+2=27$ | 22=042^2 = 0422=04
• Answer: 2704

 Square of Numbers Close to 100

For numbers close to 100 ($100\pm x$), use:

Formula:

N2=(100+x)×(100+x)=(100+2x)∣x2N^2 = (100 + x) \times (100 + x) = (100 + 2x) | x^2N2=(100+x)×(100+x)=(100+2x)∣x2

Example: 96296^2962

• $100-96=4$, so
• $(96+4)=96+4=92$ | 42=164^2 = 1642=16
• Answer: 9216

Example: 1042104^21042

• $104+4=108$ | 42=164^2 = 1642=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: $743$ → Ends in 3 →  Not a perfect square

Example: $441$ → Ends in 1 →  Perfect square (21221^2212)

 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}4489​

• First two digits → 44 (Nearest square = 62^22 = 36, 72^22 = 49)
• Last digit → 9 (So the unit place is 3 or 7)
• Check: 672=448967^2 = 4489672=4489

Answer: 67

 Estimating Square Roots of Non-Perfect Squares

Find the nearest perfect squares and use approximation.

Example: 50\sqrt{50}50​

• Nearest squares: 49(72)49 (7^2)49(72) and 64(82)64 (8^2)64(82)
• 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!

Mathematics Short Tricks/SQUARE TRICKS AND SQUARE ROOT TRICKS IN MATHEMATICS.

Vedic Mathematics Tricks and Shortcuts

Squares and Square Roots

Here are some super helpful and easy-to-remember Mathematics Short Tricks for Square and Square Root Calculations, perfect for competitive exams like SSC, Railways, Banking, and even GATE.

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SQUARE TRICKS (वर्ग करने की ट्रिक्स)

1. Square of numbers ending in 5

Trick:
If a number ends in 5, like 25, 35, 75 etc.
Use the formula:
(a5)² = a × (a+1) | 25

Examples:

• 25² = 2 × 3 = 6 ⇒ 625

• 85² = 8 × 9 = 72 ⇒ 7225

• 95² = 9 × 10 = 90 ⇒ 9025

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2. Square of numbers near 100

Trick:
Let the number be (100 ± x)
Use:
(100 + x)² = 10000 + 2×100×x + x²
(100 – x)² = 10000 – 2×100×x + x²

Examples:

• 102² = 10000 + 2×100×2 + 4 = 10404

• 98² = 10000 – 2×100×2 + 4 = 9604

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3. Square of 2-digit numbers quickly

Use the identity:
(a + b)² = a² + 2ab + b²

Example:

• 47² = (40 + 7)² = 1600 + 2×40×7 + 49 = 2209

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4. Square between two numbers

If you know:

• 30² = 900

• 31² = 961
  then estimate:
  30.5² = (30 + 0.5)² = 30² + 2×30×0.5 + 0.25 = 900 + 30 + 0.25 = 930.25

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SQUARE ROOT TRICKS (वर्गमूल निकालने की ट्रिक्स)

1. Square roots of perfect squares (up to 1000)

• Memorize squares of numbers 1–30

• Reverse lookup trick:

  • If number ends in 25 → root ends in 5

  • If number ends in 76 → root ends in 4 or 6

Example:

• √625 = 25

• √1225 = 35

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2. Square Root Estimation (Non-perfect squares)

If:

• √50 is between √49 = 7 and √64 = 8

• Use linear approximation:
  √50 ≈ 7 + (50 – 49)/[2×7] = 7 + 1/14 ≈ 7.07

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3. Shortcut Table: Squares 1–30

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Bonus Tip:

Digit Root Check for Squares:

Only numbers whose digital root is 1, 4, 7, or 9 can be perfect squares.

Example:
121 → 1+2+1 = 4 →
123 → 1+2+3 = 6 →

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Mathematics Short Tricks/SQUARE TRICKS AND SQUARE ROOT TRICKS IN MATHEMATICS.