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Question
Rationalise the denominator of the following:
`(4sqrt(3) + 5sqrt(2))/(sqrt(48) + sqrt(18))`
Solution
Let `E = (4sqrt(3) + 5sqrt(2))/(sqrt(48) + sqrt(18))`
= `(4sqrt(3) + 5sqrt(2))/(sqrt(16 xx 3) + sqrt(9 xx 2))`
= `(4sqrt(3) + 5sqrt(2))/(4sqrt(3) + 3sqrt(2))`
For rationalising the denominator, multiplying numerator and denominator by `4sqrt(3) - 3sqrt(2)`,
= `(4sqrt(3) + 5sqrt(2))/(4sqrt(3) + 3sqrt(2)) xx ((4sqrt(3) - 3sqrt(2)))/((4sqrt(3) - 3sqrt(2))`
= `(4sqrt(3)(4sqrt(3) - 3sqrt(2)) + 5sqrt(2) (4sqrt(3) - 3sqrt(2)))/((4sqrt(3))^2 - (3sqrt(2))^2` ...[Using identity, (a + b)(a – b) = a2 – b2]
= `(48 - 12sqrt(6) + 20sqrt(6) - 30)/30`
= `(18 + 8sqrt(6))/30`
= `(9 + 4sqrt(6))/15`
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