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The value of sqrt(5+2sqrt(6))-1/(sqrt(5+...

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

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`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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