How do you simplify $\frac{1}{\sqrt{2} + \sqrt{7}}$ $1/(sqrt2+sqrt7)$ ?

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How do you simplify $\frac{1}{\sqrt{2} + \sqrt{7}}$ $1/(sqrt2+sqrt7)$ ?

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Answer 1 · 2016-06-21T05:01:03

$\frac{1}{\sqrt{2} + \sqrt{7}} = \frac{\sqrt{7} - \sqrt{2}}{5}$ $1/(sqrt2+sqrt7)=(sqrt7-sqrt2)/5$

Explanation:

We simplify $\frac{1}{\sqrt{2} + \sqrt{7}}$ $1/(sqrt2+sqrt7)$ by rationalizing the denominator i.e. multiplying numerator and denominator by conjugate of denominator.

As $(\sqrt{2} + \sqrt{7})$ $(sqrt2+sqrt7)$ can be written as $(\sqrt{7} + \sqrt{2})$ $(sqrt7+sqrt2)$ and its conjugate is (sqrt7-sqrt2)#, hence

$\frac{1}{\sqrt{2} + \sqrt{7}} = \frac{1}{\sqrt{7} + \sqrt{2}}$ $1/(sqrt2+sqrt7)=1/(sqrt7+sqrt2)$

= $\frac{1 \times (\sqrt{7} - \sqrt{2})}{(\sqrt{7} + \sqrt{2}) (\sqrt{7} - \sqrt{2})}$ $(1xx(sqrt7-sqrt2))/((sqrt7+sqrt2)(sqrt7-sqrt2))$

= $\frac{\sqrt{7} - \sqrt{2}}{7 - 2} = \frac{\sqrt{7} - \sqrt{2}}{5}$ $(sqrt7-sqrt2)/(7-2)=(sqrt7-sqrt2)/5$

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