The value of `sqrt(5+2sqrt(6))-1/(sqrt(5+2sqrt(6)))` is – InterviewSolution

InterviewSolution

1.	The value of `sqrt(5+2sqrt(6))-1/(sqrt(5+2sqrt(6)))` is
Answer» `5 + 2sqrt6 = (sqrt2)^2 + (sqrt3)^2 + 2sqrt2sqrt3` so,`5 + 2sqrt6 = (sqrt2 + sqrt3)^2` now, `sqrt((sqrt2 + sqrt3)^2) - 1/sqrt((sqrt2 + sqrt3)^2)` `sqrt2 + sqrt3 - (1/(sqrt2 + sqrt3)) xx (sqrt2 - sqrt3)/(sqrt2 - sqrt3)` `sqrt2 + sqrt3 - (sqrt2 - sqrt3)/(2-3)` `sqrt2 + sqrt3 + sqrt2 - sqrt3= 2sqrt2` Answer

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