How do you solve #(sqrt6) - sqrt(3/2)#?

1 Answer

Answer:

Break the fraction under the square root sign into separate square roots, then find the common denominator and eventually get to #(sqrt(6))/2#

Explanation:

In order to subtract the fraction from the square root term, we need to have a common denominator.

Let's start with the given equation:

#sqrt(6)-sqrt(3/2)#

The key here is that the one term has a integer under the root sign and the other has a fraction. We can fix that by first taking the fraction under the square root and breaking it down into parts, like this:

#sqrt(6)-sqrt(3)/sqrt(2)#

And now we can multiply the first term by a creative form of 1 (i.e. #= sqrt(2)/sqrt(2)#) like so:

#(sqrt(6)*sqrt(2)/sqrt(2))-sqrt(3)/sqrt(2)#

#=sqrt(12)/sqrt(2)-sqrt(3)/sqrt(2)=(sqrt(12)-sqrt(3))/sqrt(2)=(2sqrt(3)-sqrt(3))/sqrt(2)=sqrt(3)/sqrt(2)#

And we can clean this up to get rid of the square root in the denominator:

#sqrt(3)/sqrt(2)*sqrt(2)/sqrt(2)=sqrt(6)/2#