How do you simplify #sqrt(4/3) -sqrt(3/4)#?

Question

18262 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-05T02:49:05

Break down the square roots, find common denominators, then combine and get to #sqrt3/6#

Let's start with the original:

#sqrt(4/3)-sqrt(3/4)#

In order to subtract the two fractions, we need a common denominator. So let's first break the square roots apart and work with the results:

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

The denominator is going to be #2sqrt3#, so let's multiply both fractions by forms of 1 to make that happen:

#2/sqrt(3)(1)-sqrt(3)/2(1)#

#2/sqrt(3)(2/2)-sqrt(3)/2(sqrt3/sqrt3)#

#4/(2sqrt(3))-3/(2sqrt3)#

#1/(2sqrt(3))#

And now we'll multiply by another form of 1 to get the square root out of the denominator:

#1/(2sqrt(3))(1)#

#1/(2sqrt(3))(sqrt3/sqrt3)#

#sqrt3/(2xx3)#

#sqrt3/6#