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

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Answer 1 · 2016-06-21T05:01:03

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

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

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

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

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

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