# How do you evaluate √50 - √ 8?

Nov 4, 2015

$3 \sqrt{2}$

#### Explanation:

It is a matter of splitting up the numbers (partitioning) into squares. These squares can then be taken out of the root.

In this case

$8 = 2 \times 4 = 2 \times {2}^{2}$
$50 = 2 \times 25 = 2 \times {5}^{2}$

So we can now write the expression as:

$\sqrt{2 \times {5}^{2}} - \sqrt{2 \times {2}^{2}}$

$5 \sqrt{2} - 2 \sqrt{2}$

$\textcolor{b l u e}{\text{Now the expression is behaving as if the } \sqrt{2}}$ $\textcolor{b l u e}{\text{is a unit of measurement}}$.

As both have the same "units" we can subtract them directly. Thus we have:

$\left(5 - 2\right) \sqrt{2} = 3 \sqrt{2}$