Albert Teen YOU ARE LEARNING:  Roots  # Roots ### Roots

The root of a number is a number which, when multiplied by itself, will make the original number.

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.

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

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

$\sqrt{25}=5$

How would you write the following phrase? "Square root of 16" 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.

$\sqrt{25}= \pm5$

1

A positive number always has two square roots

A positive and a negative Find the values of $\sqrt{36}$ Work out the values of $\sqrt{100}$ 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 $\sqrt{}$symbol.

$\sqrt{64}=4$

How would you write "the cube root of 125"? Unlike square roots, a number will only have one cube root, but we can consider positive and negative numbers. For example:

$\sqrt{-8}=-2$

1

A number only has one cube root

But it can be either POSITIVE or NEGATIVE What is the cube root of $27$? Work out the value of $\sqrt{125}$. The square root of 0 is 0. This is because: $0 \times 0 = 0$