# What is the square root of 80?

May 10, 2018

$\sqrt{80} = 4 \sqrt{5}$
$\textcolor{w h i t e}{\sqrt{80}} \approx 8.944$

#### Explanation:

By the properties of square roots:

$\sqrt{80} = \sqrt{4 \times 20}$
$\textcolor{w h i t e}{\sqrt{80}} = \sqrt{4 \times 4 \times 5}$
$\textcolor{w h i t e}{\sqrt{80}} = 4 \sqrt{5}$

An approximate decimal answer is 8.944.

May 10, 2018

sqrt80=color(blue)(4sqrt5

#### Explanation:

Given:

$\sqrt{80}$

Prime factorize $80$.

$\sqrt{2 \times 2 \times 2 \times 2 \times 5}$

Group the same prime factors in pairs.

$\sqrt{\left(2 \times 2\right) \times \left(2 \times 2\right) \times 5}$

Rewrite each pair in exponent form.

$\sqrt{{2}^{2} \times {2}^{2} \times 5}$

Apply rule: $\sqrt{{a}^{2}} = a$

$2 \times 2 \sqrt{5}$

$4 \sqrt{5}$