How do you simplify $6 \sqrt{18} + 3 \sqrt{50}$ $6sqrt18 + 3sqrt50$ ?

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How do you simplify $6 \sqrt{18} + 3 \sqrt{50}$ $6sqrt18 + 3sqrt50$ ?

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Answer 1 · 2016-06-06T15:28:38

$33 \sqrt{2}$ $33sqrt(2)$

Explanation:

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

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

This means that

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

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

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

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How do you simplify $6 \sqrt{18} + 3 \sqrt{50}$ $6sqrt18 + 3sqrt50$ ?

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How do you simplify $6 \sqrt{18} + 3 \sqrt{50}$ $6sqrt18 + 3sqrt50$ ?