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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)`
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Solution
`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)`
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