Question

rationlise the denominator​

Answer 1

Answer:

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=$\large{\frac{6-√5}{6+√5}}$

=$\large{\frac{6-√5}{6+√5}}$×$\large{\frac{6-√5}{6-√5}}$

=$\large{\frac{(6-√5)^2}{(6)^2+(√5)^2}}$

=$\large{\frac{(6)^2-2(6)(√5)+(√5)^2}{(6)^2+(√5)^2}}$

=$\large{\frac{36-12√5}{36+5}}$

=$\large{\frac{36-12√5}{41}}$

Answer 2

Answer:

$\frac{41 + 12 \sqrt{5} }{31}$

Step-by-step explanation:

$\frac{6 - \sqrt{5} }{6 + \sqrt{5} } \\ \\ = \frac{6 - \sqrt{5} }{6 + \sqrt{5} } \times \frac{6 - \sqrt{5} }{6 - \sqrt{5} } \\ \\ = \frac{(6 - \sqrt{5} ) ^{2} }{(6 + \sqrt{5} )(6 - \sqrt{5}) } \\ \\ = \frac{ {6}^{2} + ( \sqrt{5} ) ^{2} - 2 \times 6 \times \sqrt{5} }{ {6}^{2} - { (\sqrt{5} })^{2} } \\ \\ = \frac{36 + 5 - 12 \sqrt{5} }{36 - 5} \\ \\ = \frac{41 + 12 \sqrt{5} }{31}$

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