Question

\[\frac{1}{\sqrt{9} - \sqrt{8}}\] is equal to

Options

• \[3 + 2\sqrt{2}\]

• \[\frac{1}{3 + 2\sqrt{2}}\]

• \[3 - 2\sqrt{2}\]

• \[\frac{3}{2} - \sqrt{2}\]

Answer 1

Given that `1/(sqrt9- sqrt8)`

We know that rationalization factor for `sqrt9 - sqrt8` is `sqrt9 + sqrt8`. We will multiply numerator and denominator of the given expression `1/(sqrt9- sqrt8)`by `sqrt9 + sqrt8`, to get

 `1/(sqrt9- sqrt8) xx (sqrt9 + sqrt8)/(sqrt9 + sqrt8) = (sqrt9 + sqrt8)/ ((sqrt9)^2 - (sqrt8)^2) `

` = (sqrt9 + sqrt8) / (9-8)`

` = sqrt9 +sqrt2 sqrt4`

` = 3+2+sqrt2`