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

Question : 16

The square root of : ${(0.75)^3}/{1 - 0.75} + [0.75 + (0.75)^2 + 1]$ is :

a) 3

b) 2

c) 4

d) 1

Answer: (b)

Expression

= ${(0.75)^3 + (1 - 0.75)((0.75)^2 + 0.75 × 1 + {1}^2)}/{1 - 0.075}$

= ${(0.75)^3 + 1^3 - (0.75)^3}/{0.25}$

= $1/{0.25} = 100/25 = 4$

Required square root = $√{4} = 2$

Question : 17 [SSC CISF ASI 2010]

$√{1{1/4} × 64/125 × {1.44}}$ is equal to

a) $24/25$

b) $23/25$

c) 1$1/25$

d) $21/25$

Answer: (a)

Expression

= $√{5/4 × 64/125 × 1.44}$

= $√{16/25 × 144/100}$

= $4/5 × 12/10 = 24/25$

Question : 18 [SSC CGL Prelim 1999]

What is the square root of 0.09?

a) 0.03

b) 0.003

c) 0.3

d) 3.0

Answer: (c)

$√{0.09} = √{0.3 × 0.3} = 0.3$

Question : 19

The sum of $√{0.01} + √{0.81} + √{1.21} + √{0.0009}$ is :

a) 2.13

b) 2.03

c) 2.1

d) 2.11

Answer: (a)

$√{0.01} + √{0.81} + √{1.21} + √{0.0009}$

= 0.1 + 0.9 + 1.1 + 0.03 = 2.13

Question : 20 [SSC CGL Prelim 2004]

$√{{0.25}/{0.0009}} × √{{0.09}/{0.36}}$ is equal to :

a) 7$1/6$

b) 7$1/3$

c) $5/6$

d) 8$1/3$

Answer: (d)

Expression

= $√{{(0.25) × (0.09)}/{0.0009 × 0.36}}$

= $√{{25/100 × 9/100}/{9/10000 × 36/100}}$

=$√{{25 × 9 × 1000000}/{9 × 36 × 10000}}$

= ${5 × 10}/6 = 25/3 = 8{1}/3$

IMPORTANT quantitative aptitude EXERCISES

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