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Question
\[\frac{1}{\sqrt{9} - \sqrt{8}}\] is equal to
Options
\[3 + 2\sqrt{2}\]
\[\frac{1}{3 + 2\sqrt{2}}\]
\[3 - 2\sqrt{2}\]
\[\frac{3}{2} - \sqrt{2}\]
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Solution
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`
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