# How do you simplify sqrt10 times sqrt6?

Feb 4, 2016

$2 \sqrt{15}$

#### Explanation:

$\sqrt{a} \times \sqrt{b} = \sqrt{a} b \Leftrightarrow \sqrt{a} b = \sqrt{a} \times \sqrt{b}$

and $\sqrt{a} \times \sqrt{a} = a$

look for the factors of 10 and 6 , particularly 'squares'

factors of 10 are 1,2,5,10 and factors of 6 are 1,2,3,6 . Apart from 1 there are no squares and so

$\sqrt{10} = \sqrt{2} \times \sqrt{5} \textcolor{b l a c k}{\text{ and }} \sqrt{6} = \sqrt{2} \times \sqrt{3}$

$\Rightarrow \sqrt{10} \times \sqrt{6} = \sqrt{2} \times \sqrt{2} \times \sqrt{3} \times \sqrt{5}$

using the above facts simplifies to $2 \sqrt{15}$