# Rationales the Denominator and Simplify: (1 + Sqrt2)/(3 - 2sqrt2) - Mathematics

Rationales the denominator and simplify:

(1 + sqrt2)/(3 - 2sqrt2)

#### Solution

We know that rationalization factor for 3 - 2sqrt2 is 3 + 2sqrt2. We will multiply numerator and denominator of the given expression (1 + sqrt2)/(3 - 2sqrt2) by 3 + 2sqrt2

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

 = (3 + 5sqrt2 + 4)/(9 - 4 xx 2)

= (7 + 5sqrt2)/(9 - 8)

= (7 + 5sqrt2)/1

= 7 + 5sqrt2

Hence the given expression is simplified to 7 + 5sqrt2

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

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.2 | Q 4.3 | Page 14

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