# How do you multiply sqrt(-20) times sqrt(-5) ?

Aug 12, 2018

$- 10$

## First, Factor Out $i$

Negative numbers under square roots aren't pretty. Now, we know that $\sqrt{- 1} = i$, so to make things look a little nicer, let's factor that out of each expression:

$\implies i \sqrt{20} \cdot i \sqrt{5}$

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To multiply radicals, simply multiply the numbers inside them, and put a radical over the result, as shown below:

$\implies \sqrt{20} \cdot \sqrt{5}$
$= \sqrt{20 \cdot 5}$
$= \sqrt{100} = 10$

Note that you can only multiply radicals like this when the radicals are of the same power. If one of your radicals was a cube root instead of a square root, for example, you would not be able to multiply them this way.
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Lastly, Deal with $i$
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Don't forget our $i$ terms! We need to multiply these together as well:

$\implies i \cdot i = {i}^{2}$

Recall that $i = \sqrt{- 1}$, so:

${i}^{2} = {\left(\sqrt{- 1}\right)}^{2} = - 1$

Now, we just tag this on to the result from step 2, and we're done!

$\implies - 1 \cdot 10 = - 10$

Hope that helped :)