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Question
The value of \[\sqrt{5 + 2\sqrt{6}}\] is
Options
\[\sqrt{3} - \sqrt{2}\]
\[\sqrt{3} + \sqrt{2}\]
\[\sqrt{5} + \sqrt{6}\]
none of these
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Solution
Given that:`sqrt(5+2sqrt6)`.It can be written in the form `(a-b )^2 = a^2 +b^2 - 2 ab` as
`sqrt(5+2sqrt6) = sqrt(3+2+2xxsqrt3 xxsqrt2)`
` =sqrt((sqrt3)^2 + (sqrt2)^2+ 2 xx sqrt3 xxsqrt2)`
`= sqrt((sqrt3+sqrt2)^2)`
` = sqrt3 +sqrt2.`
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