How do you evaluate √2/7 - √7/2?

1 Answer
Nov 7, 2015

Answer:

There are two ways to go about this. In some problems the first works best, in others the second.

Explanation:

We first get rid of the radicals in de fractions:
#=sqrt2/sqrt7-sqrt7/sqrt2=sqrt2/sqrt7*sqrt7/sqrt7-sqrt7/sqrt2*sqrt2/sqrt2#
#=(sqrt(2*7))/(sqrt(7^2))-(sqrt(7*2))/(sqrt(2^2))=sqrt14/7-sqrt14/2#

Now we make the denominators equal:
#(2sqrt14)/14-(7sqrt14)/14=(-5sqrt14)/14=-5/14sqrt14#
You may want to write this as #-5/sqrt14#

Another solution:
First we make the denominators equal:
#=sqrt2/sqrt7-sqrt7/sqrt2=sqrt2/sqrt7*sqrt2/sqrt2-sqrt7/sqrt2*sqrt7/sqrt7#
#=(sqrt(2*2))/sqrt(7*2)-sqrt(7*7)/sqrt(7*2)=2/sqrt14-7/sqrt14#
#=-5/sqrt14#