# How do you simplify sqrt(2a^2b) times sqrt(4a^2)?

Jul 15, 2016

$\sqrt{2 {a}^{2} b} \times \sqrt{4 {a}^{2}} = 2 {a}^{2} \sqrt{2 b}$

#### Explanation:

Square Roots distribute across multiplication, that is to say:
$\sqrt{a b} = \sqrt{a} \times \sqrt{b}$

Knowing this, it's easy to see where we can simplify the given equation:
$\sqrt{2 {a}^{2} b} \times \sqrt{4 {a}^{2}}$
$= \sqrt{{a}^{2}} \times \sqrt{2 b} \times \sqrt{4} \times \sqrt{{a}^{2}}$
$= a \times \sqrt{2 b} \times 2 \times a$
$= 2 {a}^{2} \sqrt{2 b}$