Math, asked by Bratati11, 1 year ago

(root 2 /root 3)^5 × (6/7)^2

Answers

Answered by KarupsK
40
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Answered by mysticd
63

 Given \: \Big(\frac{\sqrt{2}}{\sqrt{3}}\Big)^{5} \times \Big(\frac{6}{7}\Big)^{2}

 = \frac{ \sqrt{2} \times \sqrt{2} \times\sqrt{2} \times\sqrt{2} \times \sqrt{2} }{ \sqrt{2} \times \sqrt{3} \times\sqrt{3} \times\sqrt{3} \times \sqrt{3} } \times \frac{36}{49}

 = \frac{2\times 2 \times \sqrt{2}}{3\times 3 \times \sqrt{3}} \times \frac{36}{49} \\= \frac{4\sqrt{2}}{9\sqrt{3}} \times \frac{36}{49}

/* After cancellation,we get */

 = \frac{16\sqrt{2}}{49\sqrt{3}}

Therefore.,

 \red {\Big(\frac{\sqrt{2}}{\sqrt{3}}\Big)^{5} \times \Big(\frac{6}{7}\Big)^{2}} \green {= \frac{16\sqrt{2}}{49\sqrt{3}}}

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