# How do you simplify 5sqrt3*sqrt24?

May 18, 2015

By expanding your roots and also adopting the exponential rule ${\sqrt{n}}^{2} = n$

$5 \sqrt{3} \cdot \sqrt{3 \cdot 8}$
$5 \textcolor{g r e e n}{\sqrt{3} \cdot \sqrt{3}} \sqrt{2 \cdot 4}$

We have a squared squared root, which is $= 3$

$5 \cdot 3 \cdot 4 \sqrt{2}$

Final answer: $60 \sqrt{2}$