If `x=3+2sqrt(2)` , then the value of `(sqrt(x)-1/sqrt(x))` is

Explanation

Solution:
`x=3+2sqrt(2)`
`=>1/x=1/3 +2sqrt(2)`
`=>1/x =1/3 +2sqrt(2) xx 3 -2sqrt(2)/3 -2sqrt(2)/3 +2sqrt(2)=3 +2sqrt(2)/(3^2 -(2sqrt(2))^2=`
`=3 -2sqrt(2)/9-8`
`3 -2sqrt(2)`
`:.x=1/x=3 +2sqrt(2)=3 -2sqrt(2)`
`:.x +1/x = 6`
`=>x + 1/x - 2 = 6 - 2`
`=>((sqrt(x)^2 +1/sqrt(x))^2 xx -2 xx sqrt(x) xx 1/sqrt(x)) = 4`
`=>((sqrt(x)-1/sqrt(x))^2=4`
`=>sqrt(x) - 1/sqrt(x)=+-sqrt(4)=+-2`
Hence the required answer is `2`