# How do you simplify 2sqrt6-sqrt24?

Aug 4, 2016

$0$

#### Explanation:

Write the numbers as the product of prime factors to see what we are working with..

$2 \sqrt{6} - \sqrt{24}$
=$2 \sqrt{2 \times 3} - \sqrt{\left(2 \times 2\right) \times 2 \times 3}$

=$2 \sqrt{6} - 2 \sqrt{6}$

=$0$

Aug 4, 2016

$2 \sqrt{6} - \sqrt{24} = 0$

#### Explanation:

Look for common factors

$\textcolor{b l u e}{\text{Method 1 - taking values out of the root}}$
Consider 12: this can be split into ${2}^{2} \times 6$

Write as: $2 \sqrt{6} - \sqrt{{2}^{2} \times 6}$

$\textcolor{g r e e n}{2 \sqrt{6} - 2 \sqrt{6} = 0}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{b l u e}{\text{Method 2 - taking values into the root}}$

Consider $2 \sqrt{6}$
We know that $2 = \sqrt{4} = \sqrt{{2}^{2}}$

So we have a way of taking the 2 into the square root without changing the overall value

color(brown)(2sqrt(6)-sqrt(24)color(blue)(" "->" "sqrt(2^2xx6)-sqrt(24)

But ${2}^{2} \times 6 = 4 \times 6 = 24$ giving:

$\textcolor{g r e e n}{\sqrt{24} - \sqrt{24} = 0}$