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#
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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 :)

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