Question

Rationalise the denominator of 1 + √2/5 +√2

Answer 1

Answer:

$= > \frac{3 + 4 \sqrt{2} }{23}$

Step-by-step explanation:

$Since, \: the \: denominator \: = 5 + \sqrt{2} , \\ its \: rationalizing \: factor = 5 - \sqrt{2} \\ Therefore \\ \: \frac{1 + \sqrt{2} }{5 + \sqrt{2} } = \frac{1 + \sqrt{2} }{5 + \sqrt{2} } \times \frac{5 - \sqrt{2} }{5 - \sqrt{2} } \\ = \frac{5 - \sqrt{2} + 5 \sqrt{2} - 2}{(5) {}^{2} - ( \sqrt{2}) {}^{2} } \\ = \frac{3 - \sqrt{2} + 5 \sqrt{2} }{25 - 2} \\ = \frac{3 + 4 \sqrt{2} }{23}$

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