How do you simplify sqrt(20a^13 b) * sqrt(8a^14 b^12)?

Apr 23, 2016

$4 {a}^{13} {b}^{6} \sqrt{10 a b}$

Explanation:

Look for values that can be squared. These can be taken outside the square root.

As an example, note that ${\left({a}^{2}\right)}^{7} = {a}^{2 \times 7} = {a}^{14}$

Given:$\text{ "sqrt(20a^13b)" "xx" } \sqrt{8 {a}^{14} {b}^{12}}$

Write as:$\text{ } \sqrt{{2}^{2} \times 5 \times {\left({a}^{2}\right)}^{6} \times a \times b} \times \sqrt{{2}^{2} \times 2 \times {\left({a}^{2}\right)}^{7} \times {\left({b}^{2}\right)}^{6}}$

$\implies 2 {a}^{6} \sqrt{5 a b} \times 2 {a}^{7} {b}^{6} \sqrt{2}$

$\implies 4 {a}^{13} {b}^{6} \sqrt{10 a b}$