Question

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

Answer 1

`-10`

Explanation:

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:

`=> isqrt(20) * isqrt(5)`

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

`=> sqrt(20) * sqrt(5)`
`= sqrt(20*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:

`=> i * i = i^2`

Recall that `i = sqrt(-1)`, so:

`i^2 = (sqrt(-1))^2 = -1`

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

`=> -1 * 10 = -10`

Hope that helped :)