How do you simplify sqrt(2ab^2)*sqrt(10a^5b)?

Feb 27, 2017

$= 2 {a}^{3} b \sqrt{5 b}$

Explanation:

If you are multiplying two square roots, you can combine them:

$\sqrt{a} \times \sqrt{b} = \sqrt{a b}$

$\sqrt{2 a {b}^{2}} \times \sqrt{10 {a}^{5} b} = \sqrt{20 {a}^{6} {b}^{3}}$

Write the expression as products of factors, using squares where possible:

$\sqrt{20 {a}^{6} {b}^{3}} = \sqrt{\textcolor{red}{4} \times 5 \times \textcolor{red}{{a}^{6}} \times \textcolor{red}{{b}^{2}} \times b}$

Find the square roots where possible:

$= \textcolor{red}{2 {a}^{3} b} \sqrt{5 b}$