# How do you simplify 2asqrt(9a^3b) - 3bsqrt(20a^2b) + 2asqrt(16ab)?

Mar 15, 2017

$6 {a}^{2} \sqrt{a b} - 6 a b \sqrt{5 b} + 8 a \sqrt{a b}$

#### Explanation:

Look for squared values within the roots.

$2 a \sqrt{{3}^{2} \times {a}^{2} \times a b} - 3 b \sqrt{{2}^{2} \times 5 \times {a}^{2} b} + 2 a \sqrt{{4}^{2} a b}$

$6 {a}^{2} \sqrt{a b} - 6 a b \sqrt{5 b} + 8 a \sqrt{a b}$

You could play with this further but I am not convinced it will make anything more simplified.

Example:

$2 a \sqrt{a b} \textcolor{w h i t e}{.} \left(3 a + 4\right) - 6 a b \sqrt{5 b}$