How do you simplify #1/(sqrt2+sqrt7)#?

1 Answer
Jun 21, 2016

Answer:

#1/(sqrt2+sqrt7)=(sqrt7-sqrt2)/5#

Explanation:

We simplify #1/(sqrt2+sqrt7)# by rationalizing the denominator i.e. multiplying numerator and denominator by conjugate of denominator.

As #(sqrt2+sqrt7)# can be written as #(sqrt7+sqrt2)# and its conjugate is (sqrt7-sqrt2)#, hence

#1/(sqrt2+sqrt7)=1/(sqrt7+sqrt2)#

= #(1xx(sqrt7-sqrt2))/((sqrt7+sqrt2)(sqrt7-sqrt2))#

= #(sqrt7-sqrt2)/(7-2)=(sqrt7-sqrt2)/5#