# How do you simplify square root of 24 divided by 2?

Sep 19, 2015

$\frac{\sqrt{24}}{2} = \sqrt{6}$

#### Explanation:

$\frac{\sqrt{24}}{2} = \frac{\sqrt{4 \cdot 6}}{2} = \frac{\sqrt{4} \sqrt{6}}{2} = \frac{2 \sqrt{6}}{2} = \sqrt{6}$

Mar 17, 2017

$\sqrt{6}$

#### Explanation:

What is a square root?

The square root of $16$ is $4$ because $4 \times 4 = 16$

The square root of $9$ is $3$ because $3 \times 3 = 9$

In maths: $\sqrt{49} = 7$, because $7 \times 7 = {7}^{2} = 49$

The square root of a number is another number which, multiplied by itself gives the number.

$24$ is not a square number because it does not have an exact square root. We cannot find the exact answer for it.

$\sqrt{16} = 4 \mathmr{and} \sqrt{25} = 5$, so $\sqrt{24}$ will be just less than 5.

We look at the factors of $24$ which are $1 , 2 , 3 , 4 , 6 , 8 , 12 , 24$

Notice that only $1 \mathmr{and} 4$ are square numbers.

Write $\sqrt{24}$ as factors which are squares:
" "(1 xx 24 does not help at all!!)

$\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6}$

We can work out $\sqrt{4}$, but not $\sqrt{6}$:

$\textcolor{red}{\sqrt{4} = 2}$

Now, we have to work out: $\frac{\sqrt{24}}{2}$

This is the same as: $\frac{\sqrt{4 \times 6}}{2}$ which is also $\frac{\textcolor{red}{\sqrt{4}} \times \sqrt{6}}{2}$

$= \frac{\textcolor{red}{2} \times \sqrt{6}}{2} \text{ } \leftarrow \textcolor{red}{\sqrt{4} = 2}$

$= \frac{\cancel{2} \times \sqrt{6}}{\cancel{2}} \text{ } \leftarrow$ remember $\frac{2}{2} = 1$

$= \sqrt{6}$

We cannot work this out, so leave it like this.