Question

X=8-√60 then 1÷2[√x+2/√x]

Answer 1

$Given \: \: x = 8 - \sqrt{60} = {( \sqrt{5}) }^{2} +{( \sqrt{3}) }^{2} - 2 \times \sqrt{5} \sqrt{3} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {(sqrt{5} - \sqrt{3} ) }^{2} \\ \: \: \: \: \: \: \: \sqrt{x} = \sqrt{5} - \sqrt{3} \: and \: \sqrt{5} + \sqrt{3} \\ \: \: therefore \: 1 \div 2 (\sqrt{x} + 2 \div \sqrt{x} ) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1 \div 2(2 \sqrt{5} ) = \sqrt{5} .$

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