How do you simplify  sqrt12*sqrt10?

2 Answers
Apr 22, 2016

$= \sqrt{{2}^{2} \cdot 3} \sqrt{10} = 2 \sqrt{3} \cdot \sqrt{10} = 2 \sqrt{30}$

Apr 22, 2016

Very slightly different presentation
$2 \sqrt{30}$

Explanation:

Look for common values that are in both roots. If we can find values that end being squared we can 'take them outside' the square roots.

Given:$\text{ } \sqrt{12} \sqrt{10}$

Whole number factors of 12 are:
{1,12}, {2,6}, {3,4}$\text{ }$ Note that {3,4}$\to \left\{3 , {2}^{2}\right\}$

Whole number factors of 10 are:
{1, 10}, {2,5}
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I can not spot any other possible useful combination than the following.

Write as:$\text{ } \sqrt{3 \times {2}^{2}} \times \sqrt{10}$

$2 \sqrt{3} \times \sqrt{10}$

$2 \sqrt{3 \times 10}$

$\textcolor{b l u e}{= 2 \sqrt{30}}$