# Express the Following with Rational Denominator: 1/(3 + Sqrt2) - Mathematics

Express the following with rational denominator:

1/(3 + sqrt2)

#### Solution

We know that rationalization factor for 3 + sqrt2 is 3 - sqrt2. We will multiply numerator and denominator of the given expression 1/(3 + sqrt2) by 3 - sqrt2 to get

1/(3 + sqrt2) xx (3 - sqrt2)/(3 - sqrt2) = (3 - sqrt2)/(3^2 - (sqrt2)^2)

= (3 - sqrt2)/(9 - 2)

= (3 - sqrt2)/7

Hence the given expression is simplified with rational denominator to (3 - sqrt2)/7

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

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.2 | Q 3.1 | Page 14

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