Question

`1/(sqrt(9) - sqrt(8))` is equal to ______.

Options

• `1/2(3 - 2sqrt(2))`

• `1/(3 + 2sqrt(2)`

• `3 - 2sqrt(2)`

• `3 + 2sqrt(2)`

Answer 1

`1/(sqrt(9) - sqrt(8))` is equal to `underlinebb(3 + 2sqrt(2))`.

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) = 2sqrt(2)]`

= `(3 + 2sqrt(2))/(9 - (2sqrt(2))^2`  ...[Multiplying numerator and denominator by `3 + 2sqrt(2)`]

= `(3 + 2sqrt(2))/(9 - (2sqrt(2))^2`  ...[Using identity (a – b)(a + b) = a² – b²]

= `(3 + 2sqrt(2))/(9 - 8)`

= `3 + 2sqrt(2)`