# Square roots and Cube roots

## Square Roots

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

There are two square roots for a positive number. For example, the square roots of 25 are +5 and -5. The positive square root of a number is called the principal square root.

The symbol √ is called the radical sign. The index notation is also used instead of the radical sign. For example:

= +4 can be written as = +4 .

*Example:* Find the square root of 81.

81 = 9 × 9

= 9

## Cube Roots

The cube root of a positive number ‘*N*’ is that number which, when multiplied by itself twice, gives ‘*N*’.

For example, the cube root of 8 is 2 because 2 × 2 × 2 = 8 (here 2 is being multiplied by itself twice)

The symbol for cube root is a radical sign with a small 3 on the left ∛ .

*Example:* Find the cube root of -125.

-125 = (-5)^{3} = -5 × -5 × -5

= **-5**

*Example: *Simplify: – + 4

7 × 7 × 7 = 343, so = 7

14 × 14 = 196, so = 14

so , – + 4 = 7 – 14 + 4 = 11 -14 = **-3**

### CHECK POINT

- Find the square root of 169.
- What is the cube root of 1331?
- Simplify: + – 5
- Value of –
- What is the square root of 1,024?

##### Answer key

- 13
- 11
- 1
- 12
- 32

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