Question

Simplify by rationalizing the denominator of (in the pic)..

Answer 1

Answer:

$= \frac{27 + 10 \sqrt{2} }{3}$

Step-by-step explanation:

$= \frac{5 + \sqrt{2} }{5 - \sqrt{2} }$

$= \frac{5 + \sqrt{2} }{5 - \sqrt{2} } \times \frac{5 + \sqrt{2} }{5 + \sqrt{2} }$

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

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

$= \frac{25 + 2 + 10 \sqrt{2} }{5 - 2}$

$= \frac{27 + 10 \sqrt{2} }{3}$

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Answer 2

Answer:

(27 + 10root2)/3

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