# How do you simplify  (4 sqrt12) * (3 sqrt20)?

May 27, 2016

$= 48 \sqrt{15}$

#### Explanation:

$\left(4 \sqrt{12}\right) \cdot \left(3 \sqrt{20}\right)$

$= 4 \cdot \sqrt{12} \cdot 3 \cdot \sqrt{20}$

• Simplifying both $\sqrt{12}$ and $\sqrt{20}$ by prime factorisation.

Note: Prime factorisation is expressing a number as a product of its prime factors.

• sqrt12 = sqrt (2 * 2 * 3) = sqrt (2^2 * 3 ) = color(green)(2 sqrt3

• sqrt20 = sqrt (2 * 2 * 5) = sqrt (2^2 * 5 ) = color(blue)(2 sqrt5

 4 * sqrt 12 * 3 * sqrt 20 = 4 * color(green)(2 sqrt3) * 3 * color(blue)(2 sqrt5

$4 \cdot \textcolor{b l u e}{2} \cdot \sqrt{3} \cdot 3 \cdot \textcolor{b l u e}{2} \cdot \sqrt{5} = 4 \cdot 3 \cdot \textcolor{b l u e}{2 \cdot 2} \cdot \sqrt{3} \cdot \sqrt{5}$

$= 48 \sqrt{3} \cdot \sqrt{5}$

$= 48 \sqrt{3 \cdot 5}$

$= 48 \sqrt{15}$