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

1 Answer
Darshan Senthil
Aug 12, 2018

-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
--
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 :)

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