What is $-sqrt(20) + 3 sqrt(45)$ ?

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Answer 1 · 2017-01-22T04:47:42

$7sqrt(5)$

Factor the numbers under each square root and look for "perfect square" factors
$-sqrt(color(red)((4)(5))) + 3sqrt(color(red)((9)(5)))$
Separate the terms in the square roots
$-color(red)(sqrt(4)sqrt(5))+3color(red)(sqrt(9)sqrt(5))$
Simplify the roots ( $sqrt(4)=2$ and $sqrt(9)=3$ )
$-color(red)(2)sqrt(5)+3color(red)((3))sqrt(5)$
Simplify
$-2sqrt(5)+color(red)(9)sqrt(5)$
Combine terms
$7sqrt(5)$

What is -sqrt(20) + 3 sqrt(45)-sqrt(20) + 3 sqrt(45)?