What is the square root of 5 divided by the square root of 8?

Jun 15, 2018

$\frac{\sqrt{10}}{4}$ or $\approx 0.79$

Explanation:

We have the following

$\frac{\sqrt{5}}{\sqrt{8}}$

The convention is to not have an irrational number in the denominator, so to get rid of it, we can multiply the top and bottom by $\sqrt{8}$. We get

$\frac{\sqrt{5} \cdot \sqrt{8}}{\sqrt{8}} ^ 2$

Which simplifies to

$\frac{\sqrt{40}}{8}$

We can rewrite this as

$\frac{\sqrt{4 \cdot 10}}{8}$

$\implies \frac{2 \sqrt{10}}{8}$

$\implies \textcolor{b l u e}{\frac{\sqrt{10}}{4}}$

As a decimal, this is approximately

$0.79$

Hope this helps!

Jun 15, 2018

$\frac{\sqrt{10}}{4}$

Explanation:

Let's translate this into mathematical terms:

square root of 5: $\sqrt{5}$

square root of 8: $\sqrt{8}$

Since we divide them, it becomes:
$\frac{\sqrt{5}}{\sqrt{8}}$

If you want to simplify this, we can multiply both numerator and denominator by $\sqrt{8}$:
$\frac{\sqrt{5}}{\sqrt{8}} \cdot \frac{\sqrt{8}}{\sqrt{8}}$

Simplify:
$\frac{\sqrt{40}}{8}$

$\frac{\sqrt{4 \cdot 10}}{8}$

$\frac{\sqrt{4} \sqrt{10}}{8}$

$\frac{2 \sqrt{10}}{8}$

$\frac{\sqrt{10}}{4}$

Hope this helps!