## Question

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

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

## Answers

#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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