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

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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

Concept: Operations on Real Numbers
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Chapter 3: Rationalisation - Exercise 3.2 [Page 14]

#### APPEARS IN

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

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