# 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 | |

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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 3^{2} = 9 and 4^{2} = 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.

##### Answer key

- 12.8
- 13.7
- 6.6
- 10.1
- 10.7

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