Question

Prove that :√(11+ 4√7)-√(11-4√7)= 4.​

Answer 1

Answer:

$\sqrt{11 + 4 \sqrt{7} } - \sqrt{11 - 4 \sqrt{7} } =4\\ LHS = \sqrt{7 + 4 + 4 \sqrt{7} } - \sqrt{7 + 4 - 4 \sqrt{7} } \\ = \sqrt{( \sqrt{7}) ^{2} + ( \sqrt{4}) ^{2} + 2 \times \sqrt{4} \times \sqrt{7} } \\ - \sqrt{( \sqrt{7}) ^{2} + ( \sqrt{4}) ^{2} - 2 \times \sqrt{4} \times \sqrt{7} } \\ = \sqrt{( \sqrt{7}) ^{2} + ( \sqrt{4}) ^{2} + 2 \times 2 \times \sqrt{7} } \\ - \sqrt{( \sqrt{7}) ^{2} + ( \sqrt{4}) ^{2} - 2 \times 2 \times \sqrt{7} } \\ = \sqrt{( \sqrt{7}) ^{2} + ( \sqrt{4}) ^{2} + 4 \sqrt{7} } \\ - \sqrt{( \sqrt{7}) ^{2} + ( \sqrt{4}) ^{2} - 4 \sqrt{7} } \\ = \sqrt{( \sqrt{7} + \sqrt{4} )^{2} } - \sqrt{( \sqrt{7} - \sqrt{4} )^{2} } \\ = ( \sqrt{7} + \sqrt{4} ) - ( \sqrt{7} - \sqrt{4} ) \\= \sqrt{7} + \sqrt{4} - \sqrt{7} + \sqrt{4} \\ = 2 \sqrt{4} \\ = 2 \times 2 \\ = 4</p><p>\\= RHS\\</p><p>Thus\: Proved$

Answer 2

Answer:

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