# Question f2e51

Mar 24, 2017

$\frac{5 \sqrt{2}}{16}$

#### Explanation:

You are looking for ways to split the numbers into squared values that you can 'take outside' the root

For example $25 \to {5}^{2}$ so $\sqrt{25} = \sqrt{{5}^{2}} = 5$

You can write $\sqrt{\frac{25}{128}}$ as $\frac{\sqrt{25}}{\sqrt{128}}$

If you are ever not sure about roots build a factor tree diagram (sketch) at the side of your work area. Do not forget to label it as rough work.

$\sqrt{\frac{25}{128}} \text{ "= } \frac{\sqrt{{5}^{2}}}{\sqrt{{2}^{2} \times {2}^{2} \times {2}^{2} \times 2}}$

$= \frac{5}{2 \times 2 \times 2 \times \sqrt{2}} = \frac{5}{8 \sqrt{2}}$

Mathematicians do not like roots in the denominator so lets get rid of it.

Multiply by 1 and you do not change the intrinsic value.

color(green)(5/(8sqrt(2))color(red)(xx1)" "->" "5/(8sqrt(2))color(red)(xxsqrt(2)/sqrt(2))

" "color(green)((5sqrt(2))/(8xx2)" "=" "(5sqrt(2))/16)#