# How do you simplify sqrt(6ab) * sqrt(3a)?

Jun 9, 2016

Remember that $\sqrt{A} \times \sqrt{B} = \sqrt{A \times B}$

#### Explanation:

$= \sqrt{6 a b \times 3 a} = \sqrt{18 {a}^{2} b} = \sqrt{2 \times {3}^{2} \times {a}^{2} \times b}$

We can now take out the squares to leave:

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

Jun 9, 2016

$3 a \sqrt{2 b}$

#### Explanation:

We can write the given expression as:

$\sqrt{6 a b \times 3 a}$

$= \sqrt{2 \times 3 \times a \times b \times 3 \times a}$

We can re-arrange the expression as:

$= \sqrt{2 \times \textcolor{red}{3 \times 3} \times b \times \textcolor{b l u e}{a \times a}}$

We know that $\sqrt{3 \times 3} = 3 \text{ and } \sqrt{a \times a} = a$

Therefore, we can take $3$ and $a$ out of the square root sign and the other terms remain under the square root:

$= 3 a \sqrt{2 b}$