What is the square root of 15 times (square root of 12 - square root of 15)?

1 Answer
Gió
Sep 22, 2015

I simplified up to: #6sqrt(5)-15#

Explanation:

Considering your problem as:

#sqrt(15)(sqrt(12)-sqrt(15))=#
we can multiply:

#=sqrt(15)sqrt(12)-sqrt(15)sqrt(15)=sqrt(15)sqrt(12)-15=#

because: #sqrt(15)sqrt(15)=(sqrt(15))^2=15#

Then we have:
#=sqrt(15)sqrt(12)-15=sqrt(15*12)-15=sqrt(5*3*4*3)-15=#
#=sqrt(5)sqrt(9)sqrt(4)-15=3*2sqrt(5)-15=6sqrt(5)-15#

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