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

Question : 6 [SSC CPO S.I.2006]

${(3.63)^2 - (2.37)^2}/{3.63 + 2.37}$ is simplified to

a) 1.36

b) 2.26

c) 6

d) 1.26

Answer: (d)

Using Rule 8,

Let 3.63 = a and 2.37 = b

Expression = ${a^2 - b^2}/{a + b}$

= ${(a - b)(a + b)}/{a + b}$

= a - b = 3.63 - 2.37 = 1.26

Question : 7 [SSC CGL Prelim 2000]

$(√{72} - √{18}) ÷ √{12}$ is equal to:

a) $√{3}/2$

b) $√{2}/3$

c) $√{6}$

d) $√{6}/2$

Answer: (d)

$(√{72} - √{18}) ÷ √{12}$

= ${√{72} - √{18}}/√{12}$

= ${6√{2} - 3√{2}}/{2√{3}}$

= ${3√{2}}/{2√{3}} × √{3}/√{3} = √{6}/2$

Question : 8

The value of $√{{(0.1)^2 + (0.01)^2 + (0.009)^2}/{(0.01)^2 + (0.001)^2 + (0.0009)^2}}$ is :

a) 10

b) 0.1

c) $10^2$

d) 0.01

Answer: (a)

$√{{(0.1)^2 + (0.01)^2 + (0.009)^2}/{(0.01)^2 + (0.001)^2 + (0.0009)^2}}$

= $√{{0.01 + 0.0001 + 0.000081}/{0.0001 + 0.000001 + 0.00000081}}$

= $√{{0.010181}/{0.00010181}} = √{100}$ = 10

Question : 9 [SSC CGL Prelim 2002]

The value of $√{0.000441}$ is equal to :

a) 0.0021

b) 0.021

c) 0.21

d) 0.00021

Answer: (b)

$√{0.000441}$

= $√{0.021 × 0.021}$

= 0.021

Question : 10 [SSC CGL Prelim 1999]

On simplification of ${(2.644)^2 - (2.356)^2}/{0.288}$ we get :

a) 4

b) 5

c) 1

d) 6

Answer: (b)

? = ${(2.644)^2 - (2.356)^2}/{0.288}$

= ${(2.644 - 2.356)(2.644 + 2.356)}/{0.288}$

= ${0.288 × 5}/{0.288} = 5$

Using Rule 8,
${a^2 - b^2}/{a - b} = a+b or, {a^2 - b^2}/{a + b} = a-b$

${(2.644)^2 - (2.356)^2}/{0.288}$

= ${(2.644)^2 - (2.356)^2}/{2.644 + 2.356}$

= (2.644 + 2.356) = 5

IMPORTANT quantitative aptitude EXERCISES

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