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

Express the following with rational denominator:

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

#### 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

Concept: Operations on Real Numbers
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#### APPEARS IN

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