### GCSE Maths

Numbers
Algebra
Geometry and Measures
Probability
Statistics

# Square Roots and Cube Roots

## Square Roots

The square root of a number is the value that, when squared, gives the original number. The square root is denoted as .

When we write the square root of a number, we are usually referring to both the positive and negative square roots. This is because a negative number squared is a positive number.

For example, since and , we say .

Some examples of square roots are:

• • • • ### Approximating Square Roots

For non-perfect square numbers, the square roots can be given correct to a certain number of decimal places, or correct to a certain number of significant figures. The problem will state the accuracy to be given for the answer.

Let’s look at some examples.

#### Examples

Example 1: (9 decimal places) (1 decimal place) (2 decimal places) (3 decimal places)

Example 2: (1 significant figure) (2 significant figures) (3 significant figures)

## Cube Roots

The cube root of a number is the value that, when cubed, gives the original number. The cube root is denoted as or .

Some examples of cube roots are:       ### Approximating Cube Roots

Just like square roots, cube roots of non-perfect cube numbers can be approximated to a specified number of decimal places or significant figures, as required by the problem.

Let’s look at some examples.

#### Examples

Example 1: (9 decimal places) (1 decimal place) (2 decimal places) (3 decimal places)

Example 2: (1 significant figure) (2 significant figures) (3 significant figures)