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Simplify (3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + Sqrt12/(Sqrt3 - Sqrt2) - CBSE Class 9 - Mathematics

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Question

Simplify `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + sqrt12/(sqrt3 - sqrt2)`

Solution

We know that rationalization factor for `3sqrt2 + 2sqrt3` and `sqrt3 - sqrt2` are `3sqrt2 - 2sqrt3` and `sqrt3 + sqrt2`respectively. We will multiply numerator and denominator of the given expression  `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3)` and `sqrt12/(sqrt3 - sqrt2)` by `3sqrt2 - 2sqrt3` and `sqrt3 + sqrt2` respectively to get

`(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) xx (3sqrt2 - 2sqrt3)/(3sqrt2 - 2sqrt3) + sqrt12/(sqrt3 - sqrt2) xx (sqrt3 + sqrt2)/(sqrt3 + sqrt2) = ((3sqrt2)^2 + (2sqrt3)^2 - 2 xx 3sqrt2 xx 2sqrt3)/((3sqrt2)^2 - (2sqrt3)^2) + (sqrt36 + sqrt24)/((sqrt3)^2 - (sqrt2)^2)` 

`= (18 + 12 - 12sqrt6)/(18 - 12) + (6 + sqrt24)/(3 - 2)`

`= (30 - 12sqrt6 + 36 + 12sqrt6)/6`

`= 66/6`

= 11

Hence the given expression is simplified to 11

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Solution Simplify (3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + Sqrt12/(Sqrt3 - Sqrt2) Concept: Operations on Real Numbers.
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