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# Approximating Square Roots

## Approximating Square Roots

The ‘square root’ of a given positive number ‘n’ is that number which, when multiplied by itself, gives ‘n’.

If the square root of a given number is not a whole number, then we can approximate the square root of a number.

Square Roots of Perfect Squares

 1 2 3 4 5 6 7 8 9 10 11 12

### Steps to approximate square roots:

Step 1: Think of two perfect squares between which the given number lies.

Example: If we want to find the square root of 12, then 32 = 9 and 42 = 16. So,  lies between 9 and 16.

Step 2: Divide the given number by one of the two square roots in step 1.

12 ÷ 3 = 4

Step 3: Find the average of the root and the result in step 2.

= =3.5

Step 4: Repeat steps 2 and 3 until you reach the desired result.

Repetition of step 2: 12 ÷ 3.5 = 3.4285

Repetition of step 3: === 3.46425

Now you need to decide the level accuracy to find the square root of given number. If you want it to be more accurate, keep on repeating steps 2 and 3. We leave   here.

## CHECK POINT

Find the square root of the given numbers, rounded to the nearest tenth.

1.
2.
3.
4.
5.
1.  12.8
2.  13.7
3.  6.6
4.  10.1
5.  10.7

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