Question

Simplify \sqrt{ - 180} " align="absmiddle" class="latex-formula">
show your work please ​

Answer 1

Answer: $(6\sqrt{5})i$

This is the same as saying $6i\sqrt{5}$

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Work Shown:

$\sqrt{-180} = \sqrt{-1*36*5}\\\\\sqrt{-180} = \sqrt{-1}*\sqrt{36}*\sqrt{5}\\\\\sqrt{-180} = i*6*\sqrt{5}\\\\\sqrt{-180} = 6i\sqrt{5}\\\\\sqrt{-180} = (6\sqrt{5})i$

where $i = \sqrt{-1}$

As the steps show above, the idea is to factor the radicand into smaller pieces where one of those pieces is the largest perfect square possible. In this case, 36 is the largest factor of 180 that's a perfect square. Then I used the rule $\sqrt{A*B} = \sqrt{A}*\sqrt{B}$ to break up the root.

The parenthesis used at the very end is to help separate the $6\sqrt{5}$ from the $i$ term. The "i" is not under the square root.