# How do you simplify 10/(sqrt(20)*sqrt(5)?

Dec 3, 2015

=color(blue)(1

#### Explanation:

The expression given is
$\frac{10}{\sqrt{20} \cdot \sqrt{5}}$

We first simplify the radicals by prime factorisation

• $\sqrt{20} = \sqrt{2 \cdot 2 \cdot 5} = \sqrt{{2}^{2} \cdot 5} = 2 \sqrt{5}$
• $\sqrt{5}$ is already in its simplest form.

Now, our expression becomes:

$\frac{10}{\sqrt{20} \cdot \sqrt{5}} = \frac{10}{2 \sqrt{5} \cdot \sqrt{5}}$

=10/(2*color(blue)((sqrt5*sqrt5))

$= \frac{10}{2 \cdot 5}$

$= \frac{10}{10}$

=color(blue)(1