Square root and cube root

Square root

The opposite of squaring a number is called finding the square root.

The symbol for the square root is \sqrt{}.

Diagram to show square root

Example

The square root of {16} is {4} (because 4^2 = 4 \times 4 = 16).

The square root of {25} is {5} (because 5^2 = 5 \times 5 = 25).

The square root of {100} is {10} (because 10^2 = 10 \times 10 = 100).

Question

What is the square root of {4}?

2 \times 2 = 4, so {2} is the square root of {4}.

The symbol \sqrt{} means square root, so:

\sqrt{36} means 'the square root of {36}'.

\sqrt{36} = 6

\sqrt{81} means 'the square root of {81}'.

\sqrt{81} = 9

You will also find a square root key on your calculator.

Cube root

The opposite of cubing a number is called finding the cube root.

The symbol for the cube root is ^{3}\sqrt{}.

Diagram to show cube root

Example

The cube root of {27} is {3} (because 3 \times 3 \times 3 = 27).

The cube root of {1,000} is {10} (because 10 \times 10 \times 10 = 1,000).

Question

What is the cube root of {8}?

2 \times 2 \times 2 = 8, so {2} is the cube root of {8}.

Example

The symbol ^{3}\sqrt{} means cube root, so:

\sqrt[3]{125}, means 'the cube root of {125}.

\sqrt[3]{125}=5

\sqrt[3]{64} means 'the cube root of {64}.

\sqrt[3]{64}=4