# Simplify: 3 √ 2 − 2 √ 3 3 √ 2 + 2 √ 3 + √ 12 √ 3 − √ 2 - Mathematics

Simplify: $\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}$

#### Solution

We know that rationalization factor for 3sqrt2 +2sqrt3 and  sqrt3-sqrt2are 3sqrt2 - 2sqrt3and   sqrt3 +sqrt2respectively. We will multiply numerator and denominator of the given expression  (3sqrt2 -2sqrt3)/ (3sqrt2 +2sqrt3)  and  sqrt12/(sqrt3-sqrt2)by 3sqrt2-2sqrt3and sqrt3 +sqrt2respectively, to get

(3sqrt2 -2sqrt3)/ (3sqrt2 +2sqrt3) xx (3sqrt2 -2sqrt3)/ (3sqrt2 -2sqrt3) +sqrt12/(sqrt3-sqrt2) xx (sqrt3 +sqrt2)/(sqrt3 +sqrt2) =((3sqrt2)^2+(2sqrt3)^2  - 2xx 3 sqrt2 xx 2sqrt3)/((3sqrt2)^2 -( 2sqrt3)^2 ) +(sqrt36+sqrt24)/((sqrt3)^2-(sqrt2)^2)

= (18+12-12sqrt6)/(18-12) +(6+sqrt24)/(3-2)

= (30-12sqrt6 +36 +12sqrt6)/6

=66/6

=11

Concept: Operations on Real Numbers
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.2 | Q 9.1 | Page 15

Share