Question

$7 \div 3 \sqrt{3 - 2 \sqrt{2} }$
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Answer 1

For solution , please refer to the attachment .

Answer 2

$7 \div 3 \sqrt{3 - 2 \sqrt{2} }$

$i ) \sqrt{3 - 2\sqrt{2}} \\= \sqrt{ (2+1) - 2\sqrt{2 \times 1 }} \\= \sqrt{ \sqrt{2}^{2} + 1^{2} - 2\times \sqrt{2} \times 1 }} \\= \sqrt{ (\sqrt{2} - 1)^{2}}\\= \sqrt{2} - 1 \: ---(1)$

$Now , the \: value \:of \: 7 \div 3 \sqrt{3 - 2 \sqrt{2} }\\= \frac{7}{3(\sqrt{2} - 1)} \\= \frac{7(\sqrt{2} +1)}{3(\sqrt{2} -1)(\sqrt{2}+1)}$

$= \frac{7(\sqrt{2} +1)}{3[(\sqrt{2})^{2} -1^{2}]}$

$= \frac{7(\sqrt{2} +1)}{3(2-1)}$

$= \frac{7(\sqrt{2} +1)}{3}$

Therefore.,

$\red{7 \div 3 \sqrt{3 - 2 \sqrt{2} } }$

$\green {=\frac{7(\sqrt{2} +1)}{3} }$

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