Mathematics Short Tricks/ SQUARE ROOT Tricks for Placement tricks.

Mathematics Short Tricks/ SQUARE ROOT Tricks for Placement tricks.

Square Root Tricks for Quick Calculation – Placement Exam Tips

 What is a Square Root?

The square root of a number x is a number y such that y2=xy^2 = xy2=x.
Example:
25=5\sqrt{25} = 525​=5 because 52=255^2 = 2552=25.

Square Root Short Tricks for Quick Calculation:

1. Perfect Square Method:

If the number is a perfect square, simply find its square root.

• Example: 144=12\sqrt{144} = 12144​=12
• Example: 81=9\sqrt{81} = 981​=9

2. Estimation Method for Non-Perfect Squares:

Estimate between which two perfect squares the number lies.

• Example: 50\sqrt{50}50​ lies between 72=497^2 = 4972=49 and 82=648^2 = 6482=64.
  Approximate value: 7.1 or 7.2

3. Division Method (Long Division):

Used for precise square root calculation for large numbers.

• Example: 324\sqrt{324}324​
  Divide the number into pairs from right to left: 3 | 24
  Try $1$ (1 × 1 = 1) → Subtract (3 – 1 = 2) → Bring down 24 → Try 8 (28 × 8 = 224)
  Answer: 18

4. Using Unit Digit Analysis:

Perfect squares end in 0, 1, 4, 5, 6, 9. Use this to find the square root.

• Example: Find 784\sqrt{784}784​
  Last digit 4 means root ends in 2 or 8.
  282=78428^2 = 784282=784 ⇒ Answer: 28

5. Quick Trick for Numbers between 40-60:

Use the formula:
(a2+b)≈a+b2a\sqrt{(a^2 + b)} \approx a + \frac{b}{2a}(a2+b)​≈a+2ab​
where $a$ is the nearest perfect square root and $b$ is the difference.

• Example: 47\sqrt{47}47​
  Nearest perfect square = 49 (7²)
  $49-47=2$
  47≈7−214=7−0.14=6.86\sqrt{47} \approx 7 – \frac{2}{14} = 7 – 0.14 = 6.8647​≈7−142​=7−0.14=6.86

6. Shortcut for Decimal Square Roots:

To find the square root of decimals, make pairs from the decimal point.

• Example: 0.0049\sqrt{0.0049}0.0049​
  Pairs: $49$ — Square root of 49 is 7
  Decimal places = 4, so square root will have 2 decimal places.
  Answer: 0.07

 Practice Questions:

1. 361\sqrt{361}361​ = ?
2. 225\sqrt{225}225​ = ?
3. 0.0025\sqrt{0.0025}0.0025​ = ?
4. 18\sqrt{18}18​ (approx.) = ?
5. 625\sqrt{625}625​ = ?

If you need more detailed methods or have specific questions, just let me know!

Mathematics Short Tricks/ SQUARE ROOT Tricks for Placement tricks.

Short tricks to calculate square roots – googleapis.com

Sure! Here’s a collection of super fast and easy square root tricks — perfect for placements, aptitude tests, and competitive exams like SSC, Bank, Campus Recruitment, etc.

Mathematics Short Tricks: Square Root Tricks for Placements

Trick #1: Perfect Square Identification (Last Digit Trick)

Check if a number is a perfect square by its last digit.

Example: Is 784 a perfect square?

• Last digit is 4 → must end in 2 or 8

• √784 = 28

Trick #2: Find Square Root of a Perfect Square (2-Digit Numbers)

Example: √1521

1. Last digit = 1, possible unit digits = 1 or 9

2. Nearest square below 1521 is 1444 → √1444 = 38

3. Try both:

   • 39² = 1521

   • So √1521 = 39

Trick #3: Estimation for Non-Perfect Squares

Example: √50

• Perfect squares around 50: √49 = 7, √64 = 8

• So √50 ≈ 7.0 – 7.1

• Try 7.1² = 50.41 → Close enough

Use this for quick estimation in MCQs.

Trick #4: Square Root of Numbers Ending with 25

Formula:

√(x×100 + 25) = 10x + 5, if the number is a perfect square

Example: √1225

• 1225 = (12 × 100 + 25)

• So √1225 = 10×12 + 5 = 125

Trick #5: For Square Roots of Fractions

√(a/b) = √a / √b

Example: √(49/16) = √49 / √16 = 7 / 4

Practice Questions:

1. √2025 = ?

2. √1369 = ?

3. Which is closer to √82: 9 or 9.1?

4. Is 9801 a perfect square?

Want More?

I can provide:

• PDF of these tricks with examples

• Video explanation

• Quiz on square root tricks

Let me know how you’d like to practice!