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

#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))#