Model 2 Simplification based on square & square root Practice Questions Answers Test with Solutions & More Shortcuts
simplification PRACTICE TEST [4 - EXERCISES]
Model 1 Simplification using VBODMAS
Model 2 Simplification based on square & square root
Model 3 Simplification based on cube & cube root
Model 4 Simplification with continued fraction
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 »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 »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 »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 »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 »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
Model 2 Simplification based on square & square root Shortcuts »
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