What is the square root of 10 times the square root of 20?

1 Answer
Stefan V.
Sep 9, 2015

10sqrt(2)

Explanation:

You need to multiply sqrt(10) and sqrt(20).

Before doing that, take a look at sqrt(20). Notice that you can write it as

sqrt(20) = sqrt(2 * 10)

If you use the product property of radicals, which tells you that

color(blue)(sqrt(a * b) = sqrt(a) * sqrt(b))

you can write

sqrt(2 * 10) = sqrt(2) * sqrt(10).

Your expression will now be

sqrt(10) * sqrt(2) * sqrt(10) = sqrt(2) * sqrt(10) * sqrt(10)

=sqrt(2) * sqrt(10 * 10) = sqrt(2) * sqrt(100)

= sqrt(2) * 10 = color(green)(10sqrt(2))

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