How do you simplify the square root of 40?

Sep 16, 2015

$2 \sqrt{10}$

Explanation:

$\sqrt{40}$

Write the prime factors for $40$.

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

Group the same prime factors into pairs.

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

Rewrite $\left(2 \times 2\right)$ in exponent form.

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

Apply the rule $\sqrt{{x}^{2}} = x$

$\sqrt{{2}^{2}} = 2$

Simplify.

$2 \sqrt{2 \times 5}$

Simplify.

$2 \sqrt{10}$