`1/(sqrt(9)-\ sqrt(8))` is equal?

Options

A. `1/2 (3-2sqrt(2))`
B. `1/(3+2sqrt(2))`
C. `3-2sqrt(2)`
D. `3+2sqrt(2)`

Answer

D

Explanation

`(1)/(sqrt(9) - sqrt(8)) = (1)/(3-2sqrt(2)) = (1)/(3-2sqrt(2)) . (3+2sqrt(2))/(3+2sqrt(2)) , [:' sqrt(8) = sqrt(2 xx 2 xx 2) = 2 sqrt(2)]`
[multilplying numerator and denominator by `3+2sqrt(2)`]
`= (3+2sqrt(2))/(9-(2sqrt(2))^(2))` , [using identify `(a-b)(a+b) = a^(2) - b^(2)`]
`= (3+2sqrt(2))/(9-8) = 3+2sqrt(2)`