# Rationales the Denominator and Simplify: (2sqrt3 - Sqrt5)/(2sqrt2 + 3sqrt3) - Mathematics

Rationales the denominator and simplify:

(2sqrt3 - sqrt5)/(2sqrt2 + 3sqrt3)

#### Solution

We know that rationalization factor for 2sqrt2 + 3sqrt3 is 2sqrt2 - 3sqrt3. We will multiply numerator and denominator of the given expression (2sqrt3 - sqrt5)/(2sqrt3 + 3sqrt3) by 2sqrt2 - 3sqrt3 to get

(2sqrt3 - sqrt5)/(2sqrt2 + 3sqrt3) xx (2sqrt2 - 3sqrt3)/(2sqrt2 - 3sqrt3) = (2 xx 2 xx sqrt3 xx sqrt2 - 2 xx 3 xx sqrt3 xx sqrt3 - 2 xx sqrt5 xx sqrt2 + 3 xx sqrt5 xx sqrt3)/((2sqrt2)^2 - (3sqrt3)^2)

= (4sqrt(3 xx 2) - 6 xx (sqrt3)^2 - 2 xx sqrt(5 xx 2) + 3 xx sqrt(5 xx 3))/(4 xx 2 - 9 xx 3)

= (4sqrt6 - 6 xx 3 - 2sqrt10 + 3 sqrt15)/(8 - 27)

= (4sqrt6 - 18 - 2sqrt10 + 3sqrt15)/(-19)

= (18 + 2sqrt10 - 3sqrt15 - 4sqrt6)/19

Hence the given expression is simplified to (18 + 2sqrt10 - 3sqrt15 - 4sqrt6)/19

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

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.2 | Q 4.6 | Page 14

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