# What is the square root of 20 times the square root of 15?

Sep 8, 2015

sqrt(4*5)*sqrt(15)=color(green)( 10sqrt 3 ~ 17.321

#### Explanation:

square root of 20 times the square root of 15 in mathematical terms can be written as $\sqrt{20} \cdot \sqrt{15}$

=$\sqrt{4 \cdot 5} \cdot \sqrt{15}$

We know that $\textcolor{b l u e}{\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}}$

Hence =$\sqrt{4 \cdot 5} \cdot \sqrt{15} = \sqrt{4} \cdot \sqrt{5} \cdot \sqrt{3} \cdot \sqrt{5}$

$= 2 \cdot {\left(\sqrt{5}\right)}^{2} \cdot \sqrt{3}$

$= 2 \cdot 5 \cdot \sqrt{3}$

 =color(green)( 10sqrt 3