How do you simplify $6sqrt18 + 3sqrt50$ ?

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Answer 1 · 2016-06-06T15:28:38

$33sqrt(2)$

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

$sqrt(18) = sqrt(2 times 3^2) = sqrt(2)sqrt(3^2) = 3sqrt(2)$

and similarly, $sqrt(50) = 5sqrt(2)$ .

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

How do you simplify 6sqrt18 + 3sqrt506sqrt18 + 3sqrt50?