# The Value of √ 48 + √ 32 √ 27 + √ 18 is - Mathematics

MCQ

The value of $\frac{\sqrt{48} + \sqrt{32}}{\sqrt{27} + \sqrt{18}}$ is

#### Options

• $\frac{4}{3}$

• 4

• 3

• 3/4

#### Solution

Given that (sqrt48+sqrt32)/(sqrt27 +sqrt18)

We know that rationalization factor for  sqrt27 +sqrt18 issqrt27 - sqrt18  We will multiply numerator and denominator of the given expression (sqrt48+sqrt32)/(sqrt27 +sqrt18) bysqrt27 - sqrt18, to get

(sqrt48+sqrt32)/(sqrt27 +sqrt18) xx  (sqrt27-sqrt18)/(sqrt27 -sqrt18) = (sqrt48 xx sqrt27 - sqrt48 xx sqrt18 + sqrt32 xx sqrt27 - sqrt32 xx sqrt18)/ ((sqrt27)^2 - (sqrt18)^2)

We can factor irrational terms as

 (sqrt(3) xx sqrt16 xx sqrt9 xx sqrt3 - sqrt3 xx sqrt16 xx sqrt9 xx sqrt2 +sqrt2 xx sqrt16 xx sqrt3  xx sqrt9 - sqrt2 xx sqrt16 xx sqrt9 xx sqrt2)/((sqrt27)^2 - (sqrt18)^2)

= ((sqrt3)^2 xx 4 xx 3 - sqrt(3xx2)xx 4 xx 3 + sqrt(2 xx3) xx 4 xx3 - (sqrt2)^2 xx 4 xx 3)/(27-18)

= (3xx12-12xxsqrt6+12 xxsqrt6 -2 xx12)/(27-18)

= (36-12sqrt6+12sqrt6-24)/(27-18)

= 12/9

 = 4/3

Concept: Laws of Exponents for Real Numbers
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Chapter 3: Rationalisation - Exercise 3.4 [Page 17]

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.4 | Q 16 | Page 17

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