# Square Root : Find square Root of any number in a 5 seconds

## Square number

A square number or perfect square is the product of some integer with itself. For example, 25 is a square number, since it can be written as 5 × 5.

## How to find Square of a Number

To Find square of a number, just multiply it by itself.

For Example, square of 2 is 2 x 2 = 4

## Square Root

The square root of a number is a value that, when multiplied by itself, gives the number.

## Square Root Symbol

The symbol of Square root is √

## Finding Square Roots

The easiest way to find a square root is to use a calculator, but you can do it without one. Here’s one way, using 12 as an example of the squared number:

✓ Pick a number that when squared, comes close to (but is less than) the number whose square root you’re finding: 3 x 3 = 9. This is a better choice than 4: 4 × 4 = 16

✓ Divide the number you’re finding the square root of (12) by the number you squared (3) in step 1: 12 ÷ 3 = 4
✓ Average the closest square root (3) and the answer of step 2 (4): 3 + 4 = 7. 7 ÷ 2 = 3.5
✓ Square the average to see how close the number is to 12:

3.5 × 3.5 = 12.25—Close, but not close enough!

Repeat steps 2 and 3 until the number squared is very close to 12:

Divide: 12 ÷ 3.5 = 3.43

Average: 3.5 + 3.43 = 6.935

6.935 ÷ 2 = 3.465

3.465 × 3.465 = 12.006, close enough!

## Problems based on Square Root

How to Calculate Square of a Number

Example1: 6 × 6 = 36, so a square root of 36 is 6.

Example2: √25 = 5 (because 5 x 5 = 25)

Example3: √9 = 3 (because 3 x 3 = 9 )

Example 4: √256 = 16 (because 16 x 16 = 256 )

Example 5: √2500 = 50 (because 50 x 50 = 2500)

Example 6: √3025 = 55 (because 55 x 55 = 3025)

Example 7: √4489 = 67 (because 67 x 67 = 4489)

Example 8: √7744 = 88 (because 88 x 88 = 7744)

Example 9: √8649 = 93 (because 93 x 93 = 8649)

Example 10: √10000 = 100 (because 100 x 100 = 10000)

Note:
1. We can also square negative numbers.
For Example (-3) X (-3)= 9

2. Square Root is also applied for decimals
For Example √15.5 = 3.94

## Perfect Square

A number made by squaring a whole number (0,1,2,3,4_ _ _ _)

For Example 9 is a perfect square because it can be expressed as 3 x 3 (the product of two equal integers)

16 is a perfect square because it can be expressed as 4 * 4 (the product of two equal integers)

## Square roots of numbers 1-100

Given below are the square numbers up to 100

 Number Square Square root 1 1 1.000 2 4 1.414 3 9 1.732 4 16 2.000 5 25 2.236 6 36 2.449 7 49 2.646 8 64 2.828 9 81 3.000 10 100 3.162 11 121 3.317 12 144 3.464 13 169 3.606 14 196 3.742 15 225 3.873 16 256 4.000 17 289 4.123 18 324 4.243 19 361 4.359 20 400 4.472 21 441 4.583 22 484 4.690 23 529 4.796 24 576 4.899 25 625 5.000 26 676 5.099 27 729 5.196 28 784 5.292 29 841 5.385 30 900 5.477 31 961 5.568 32 1,024 5.657 33 1,089 5.745 34 1,156 5.831 35 1,225 5.916 36 1,296 6.000 37 1,369 6.083 38 1,444 6.164 39 1,521 6.245 40 1,600 6.325 41 1,681 6.403 42 1,764 6.481 43 1,849 6.557 44 1,936 6.633 45 2,025 6.708 46 2,116 6.782 47 2,209 6.856 48 2,304 6.928 49 2,401 7.000 50 2,500 7.071 51 2,601 7.141 52 2,704 7.211 53 2,809 7.280 54 2,916 7.348 55 3,025 7.416 56 3,136 7.483 57 3,249 7.550 58 3,364 7.616 59 3,481 7.681 60 3,600 7.746 61 3,721 7.810 62 3,844 7.874 63 3,969 7.937 64 4,096 8.000 65 4,225 8.062 66 4,356 8.124 67 4,489 8.185 68 4,624 8.246 69 4,761 8.307 70 4,900 8.367 71 5,041 8.426 72 5,184 8.485 73 5,329 8.544 74 5,476 8.602 75 5,625 8.660 76 5,776 8.718 77 5,929 8.775 78 6,084 8.832 79 6,241 8.888 80 6,400 8.944 81 6,561 9.000 82 6,724 9.055 83 6,889 9.110 84 7,056 9.165 85 7,225 9.220 86 7,396 9.274 87 7,569 9.327 88 7,744 9.381 89 7,921 9.434 90 8,100 9.487 91 8,281 9.539 92 8,464 9.592 93 8,649 9.644 94 8,836 9.695 95 9,025 9.747 96 9,216 9.798 97 9,409 9.849 98 9,604 9.899 99 9,801 9.950 100 10,000 10.000

# Find Square Root Quickly

Watch the video below to learn some quick  tricks for calculation of square root.