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Express the Following with Rational Denominator: (6 - 4sqrt2)/(6 + 4sqrt2) - Mathematics

Express the following with rational denominator:

`(6 - 4sqrt2)/(6 + 4sqrt2)`

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Solution

We know that rationalization factor for `6 + 4sqrt2` is `6 - 4sqrt2`. We will multiply numerator and denominator of the given expression `(6 - 4sqrt2)/(6 + 4sqrt2)` by `6 - 4sqrt2` to get

`(6 - 4sqrt2)/(6 + 4sqrt2) xx (6 - 4sqrt2)/(6 - 4sqrt2) = (6^2  + (4sqrt2)^2 - 2 xx 6 4 sqrt2)/((6)^2 - (4sqrt2)^2)`

` (36 + 16 xx 2 - 48sqrt2)/(36 - 16 xx 2)`

`= (36 + 32 - 48sqrt2)/(36 - 32)`

`= (68 - 48sqrt2)/4`

`= 17 - 12sqrt2`

Hence the given expression is simplified with rational denominator to `17 - 12sqrt2`

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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.2 | Q 3.7 | Page 14
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