powers & roots

A power is a small number written above a base number that indicates how many times to multiply the base by itself.

The base is multiplied by itself the number of times indicated by the power. 

We say "5 to the power of 3"  or  "7 to the power of 5".

Another word for power is index or exponent. 

If we have a power of 2, we often say "squared".

This is because multiplying the same number by itself is the same as working out the area of a square.

eg 4 to the power of 2 = 4 squared.

If we have a power of 3, we often say "cubed".

This is because multiplying the same number by itself three times is the same as working out the volume of a cube.

eg 2 to the power of 3 = 2 cubed.

The opposite operation of powers is roots. A root is a number that when multiplied by itself a number of times gives us the original number.

The root symbol looks like:

If there is no number alongside the root sign, then we know it is a square root. This is the opposite to squaring a number, or raising the number to the power of 2. We are looking for a number that multiplies by itself to get the original number.

Example

The square root of 25 = 5, because 5 ✕ 5 = 25.

We should technically put the 2 alongside (up high like a power) next to the root sign to indicate it is a square root, but no-one does this as we know it means square root.

If there is a number alongside the root sign, then we know it is a root to that number. We are looking for a number that multiplies by itself by the number of times indicated to get the original number.

If it is a three, we call it a cube root.

If it is any other number we call it the nth root.

Example

The cube root of 216 = 6, because 6 ✕ 6 ✕ 6 = 216.