Question

Simplify by rationalizing the denominator : 1/5+√2

Answer 1

hooe this answer helped you

Answer 2

Answer:  

  $\frac{5-\sqrt{2} }{23}$ is the final answer.

Step-by-step explanation:

• Rationalise    $\frac{1}{5+\sqrt{2} }$

Whenever there is root present in denominator, we try to remove root from denominator by rationalising it.

In this case, Multiply both numerator and denominator by $5-\sqrt{2}$. This step is called rationalising the deominator.

                           $\frac{1}{5+\sqrt{2} } = \frac{1 * (5-\sqrt{2}) }{(5+\sqrt{2})*(5-\sqrt{2)} }$

                            $\frac{1}{5+\sqrt{2} } = \frac{(5-\sqrt{2}) }{5^{2}- (\sqrt{2} )^{2} } }$

                         $\frac{(5-\sqrt{2}) }{5^{2}- (\sqrt{2} )^{2} } } = \frac{(5-\sqrt{2}) }{25- 2 } }$

                           $\frac{(5-\sqrt{2}) }{25- 2 } } = \frac{(5-\sqrt{2}) }{23} }$

                           $\frac{(5-\sqrt{2}) }{23} } = \frac{5}{23}- \frac{\sqrt{2} }{23}$

Therefore, the final answer after rationalisation is  $\frac{5-\sqrt{2} }{23}$.

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