# 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**

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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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__Arithemetic & Pre Algebra__

**The Number System**

1) Rational and Irrational Numbers

2) Compare Irrational Numbers

3) Fractions and Repeating Decimals

4) Approximating Square Roots

__Algebra__

**Expressions and Equations**

1) Exponents and their properties

2) Square roots and Cube roots

3) Scientific Notation – addition, subtraction, division and multiplication

4) Equations with variables on both sides

5) Linear equations with one, zero, or infinite solutions

6) Age Word Problems

7) Solve systems of linear equations with elimination and substitution

8) Word Problems on System of Linear Equations

__Geometry__

1) Parallel Lines

2) Congruent Angles

3) Finding Angle Measures

4) Pythagorean Theorem

5) Distance Formula

6) Word problems on Volume of Cones, Cylinders, and Spheres

__Statistics and Probability__