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# 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

1. Find the square root of 169.
2. What is the cube root of 1331?
3. Simplify: + – 5
4. Value of – 5. What is the square root of 1,024?
1. 13
2. 11
3. 1
4. 12
5. 32

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