Roots

Roots reverse the process of indices, to find the original number.

Imagine a number, let's call it $x$. If we multiply this by itself we get $x^2$. This is the square number.

$x$ would be the square root as it is the number that was originally squared.

Let's think about this concept with numbers.

The square root of $25$ is $5$ because we know that $5 \times 5 = 25$

We can denote this with a $\sqrt{}$ sign:

$\sqrt{25}=5$

Multiplying two negatives together gives a positive number. Therefore,$25$ has another root:

$-5 \times -5=25$

We can describe the positive and negative square roots with a $\pm$ sign - this indicates both a positive and a negative option.

$\sqrt{25}= \pm5$

A cube root of a number is a number which, when multiplied by itself 3 times, generates the original number. The cube root of 64 is 4.

$4 \times 4\times4=64$

We indicate a cube root with the $\sqrt[3]{}$symbol.

$\sqrt[3]{64}=4$

Unlike square roots, a number will only have one cube root, but we can consider positive and negative numbers. For example:

$\sqrt[3]{-8}=-2$

The square root of 0 is 0. This is because: $0 \times 0 = 0$