Question

rationalize the denominator of 5+root2 / 3+root2

Answer 1

Answer:

refer the attachment

Step-by-step explanation:

rationalize the denominator of 5+root2 / 3+root2

Answer 2

Answer:

$\frac{5 + \sqrt{2}}{3 + \sqrt{2} } \\ rationalising \: the \: denominator \\ \frac{5 + \sqrt{2} }{3 + \sqrt{2} } \times \frac{3 - \sqrt{2} }{3 - \sqrt{2} } \\ = \frac{(5 + \sqrt{2})(3 - \sqrt{2}) }{ {3}^{2} - ( {\sqrt{2)}^{2} } } \\ = \frac{5(3 - \sqrt{2}) + \sqrt{2}(3 - \sqrt{2})}{9 - 2} \\ = \frac{15 - 5 \sqrt{2} + 3 \sqrt{2} -{ ( \sqrt{2} )}^{2} }{7} \\ = \frac{15 - 2 \sqrt{2} - 2 }{7} \\ = \frac{13 - 2 \sqrt{2} }{7} \\ \red{\frak{which \:is \: the \: required \: answer. }}$

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