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

Answer 1

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.`