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Rationales the Denominator and Simplify: (3 - Sqrt2)/(3 + Sqrt2) - Mathematics

Rationales the denominator and simplify:

`(3 - sqrt2)/(3 + sqrt2)`

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Solution

We know that rationalization factor for `sqrt3 + sqrt2` is "sqrt3 - sqrt2". We will multiply numerator and denominator of the given expression `(sqrt3 - sqrt2)/(sqrt3 + sqrt2)` by `sqrt3 - sqrt2` to get

`(sqrt3 - sqrt2)/(sqrt3 + sqrt2) xx (sqrt3 - sqrt2)/(sqrt3 - sqrt2) = ((sqrt3)^2 + (sqrt2)^2 - 2 sqrt3 xx sqrt2)/((sqrt3)^2 - (sqrt2)^2)` 

`= (3 + 2 - 2sqrt6)/(3 - 2)`

`= (5 - 2sqrt6)/1`

`= 5 - 2sqrt6`

Hence the given expression is simplified to `5 - 2sqrt6`

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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.2 | Q 4.1 | Page 14
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