# How do you simplify  ( 10sqrt 2)/(2 sqrt 8)?

Apr 16, 2016

$\frac{18 \sqrt{2}}{2 \sqrt{8}} = \frac{9 \sqrt{2}}{2 \sqrt{2}} = 4.5$

Apr 16, 2016

$\pm \frac{5}{2}$

#### Explanation:

Write as

$\frac{10 \sqrt{2}}{2 \sqrt{2} \sqrt{4}} \to \frac{10 \sqrt{2}}{4 \sqrt{2}} \to \frac{10}{4} \times 1 = \frac{5}{2}$

Consider: $\left(- a\right) \times \left(- a\right) = \left(+ a\right) \times \left(+ a\right) = {a}^{2}$. The example's ${a}^{2}$ is the equivalent condition to the 8 and 2 in $\sqrt{2} \text{ and } \sqrt{8}$. So in our solution the square root cane be positive or negative. Thus our answer is:

$\text{ } \pm \frac{5}{2}$