# How do you simplify sqrt(5/4)?

Feb 13, 2016

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

#### Explanation:

Write as :$\text{ " (sqrt(5))/(sqrt(4)) " "=" "(sqrt(5))/(sqrt(2^2)) " "=" } \frac{1}{2} \times \sqrt{5}$

Or $\text{ } \frac{\sqrt{5}}{2}$

Feb 13, 2016

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

#### Explanation:

$\frac{\sqrt{5}}{4}$

since $\sqrt{\frac{a}{b}}$ = $\frac{\sqrt{a}}{\sqrt{b}}$,

we can evaluate first the numerator, the upper part of a fraction

$\sqrt{5}$, as it is not a "perfect square", perfect squares are like
$2 \cdot 2 = 4$
$3 \cdot 3 = 9$
$4 \cdot 4 = 16$
and so on...

since $\sqrt{5}$ is not a perfect square, it will still remain not simplified.

then we proceed to the denominator, the lower part of a fraction.
$\sqrt{4}$

since $4$ is a perfect square, $2 \cdot 2 = 4$

we can get $\sqrt{4} = 2$,

plugging all the answers, we get

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

:)