# How do you simplify 6sqrt18 + 3sqrt50?

Jun 6, 2016

$33 \sqrt{2}$

#### Explanation:

Consider $18$ and $50$ as products of primes:

$18 = 2 \times 9 = 2 \times {3}^{2}$ and $50 = 2 \times 25 = 2 \times {5}^{2}$

This means that

$\sqrt{18} = \sqrt{2 \times {3}^{2}} = \sqrt{2} \sqrt{{3}^{2}} = 3 \sqrt{2}$

and similarly, $\sqrt{50} = 5 \sqrt{2}$.

Thus, $6 \sqrt{18} + 3 \sqrt{50}$ can be simplified as such:
$6 \sqrt{18} + 3 \sqrt{50}$ = $6 \left(3 \sqrt{2}\right) + 3 \left(5 \sqrt{2}\right) = 18 \sqrt{2} + 15 \sqrt{2} = 33 \sqrt{2}$