How do you simplify: the square root of -125?

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How do you simplify: the square root of -125?

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Answer 1 · 2015-07-16T19:45:18

$5 i \cdot \sqrt{5}$ $5i*sqrt(5)$

Explanation:

Let's break this into it's factors:

$\sqrt{- 125} = \sqrt{- 1 \cdot 5 \cdot 5 \cdot 5} = \sqrt{- 1} \cdot \sqrt{5} \cdot \sqrt{5^{2}}$ $sqrt(-125)=sqrt(-1*5*5*5)=sqrt(-1)*sqrt(5)*sqrt(5^2)$

We can evaluate the first and 3rd terms here to give:
$\sqrt{- 1} \cdot \sqrt{5} \cdot \sqrt{5^{2}} = 5 i \cdot \sqrt{5}$ $sqrt(-1)*sqrt(5)*sqrt(5^2)=5i*sqrt(5)$

Where $i = \sqrt{- 1}$ $i=sqrt(-1)$ (a concept from complex analysis).

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How do you simplify: the square root of -125?

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