Model 2 Simplification based on square & square root Practice Questions Answers Test with Solutions & More Shortcuts

Question : 26 [SSC CGL Prelim 2003]

The value of ${0.051 × 0.051 × 0.051 + 0.041 × 0.041 × 0.041}/{0.051 × 0.051 - 0.051 × 0.041 + 0.041 × 0.041}$ is :

a) 0.092

b) 0.0092

c) 0.92

d) 0.00092

Answer: (a)

Using Rule 4,
FORMULA → ${a^3 + b^3}/{a^2 - ab + b^2}$ = (a + b)

Let 0.051 = x and 0.041 = y

The given expression

= ${x^3 + y^3}/{x^2 - xy + y^2}$

= ${(x + y)(x^2 - xy + {y}^2)}/{x^2 - xy + {y}^2}$

= x + y

= 0.051 + 0.041 = 0.092

Question : 27

$[2√{54} - 6√{2/3} - √{96}]$ is equal to

a) 1

b) 2

c) 0

d) $√6$

Answer: (c)

Expression

= $2√{54} - 6√{2/3} - √{96}$

= $2√{9 × 6} - √{{2 × 6 × 6}/3} - √{16 × 6}$

= $2 × 3√{6} - 2√{6} - 4√{6}$ = 0

Question : 28 [SSC CPO S.I.2003]

The value of ${4 - √{0.04}}/{4 + √{0.4}}$ is close to

a) 0.8

b) 1.0

c) 0.4

d) 1.4

Answer: (a)

${4 - √{0.04}}/{4 + √{0.4}} = {4 - 0.2}/{4 + √{0.4}}$

= ${3.8}/{4 + 0.632} = {3.8}/{4.632} = 0.8$

= (a + b) = 0.08 + 0.02 = 0.1

Question : 29

The value of $√{0.441}/√{0.625}$ is equal to :

a) 0.84

b) 0.48

c) 0.048

d) 0.084

Answer: (a)

Expression = $√{0.441}/√{0.625}$

= $√{{0.441}/{0.625}} = √{441/625}$

= $21/25$ = 0.84

Question : 30 [SSC CGL Prelim 2002]

The value of $√{{(0.03)^2 + (0.21)^2 + (0.065)^2}/{(0.003)^2 + (0.021)^2 + (0.0065)^2}}$ is :

a) 10

b) $10^2$

c) 0.1

d) $10^3$

Answer: (a)

Let 0.03 = x ⇒ 0.003 = $x/10$

0.21 = y ⇒ 0.021 = $y/10$

and 0.065 = z ⇒ 0.0065= $z/10$

Expression

= $√{{x^2 + y^2 + z^2}/{(x/10)^2 + (y/10)^2 + (z/10)^2}}$

= $√{100{(x^2 + y^2 + z^2)}/ {(x^2 + y^2 + z^2)}}$

= $√{100}$ = 10

IMPORTANT quantitative aptitude EXERCISES

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