Model 2 Simplification based on square & square root Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 4 EXERCISES
The following question based on simplification topic of quantitative aptitude
(a) 0.004
(b) 0.4
(c) 0.02
(d) 0.04
The correct answers to the above question in:
Answer: (d)
${(0.03)^2 - (0.01)^2}/{0.03 - 0.01}$
[Using ${a^2 - b^2}$ = (a + b)(a - b)]
= ${(0.03 + 0.01)(0.03 - 0.01)}/{0.03 - 0.01}$
= 0.03 + 0.01 = 0.04
Using Rule 8,
${(0.03)^2 - (0.01)^2}/{0.03 - 0.01}$
= (0.03 + 0.01 = 0.04
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Read more problems based on squares and roots Based Quantitative Aptitude Questions and Answers
Question : 1
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 »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 : 2
$[2√{54} - 6√{2/3} - √{96}]$ is equal to
a) 1
b) 2
c) 0
d) $√6$
Answer »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 : 3
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 »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 : 4
The square root of $({272}^2 - {128}^2)$ is :
a) 200
b) 240
c) 256
d) 144
Answer »Answer: (b)
? = $√{({272}^2 - {128}^2)}$
= $√{(272 + 128)(272 + 128)}$
= $√{400 × 144}$ = 20 × 12 = 240
Question : 5
$√{{0.009 × 0.036 × 0.016 × 0.08}/{0.002 × 0.0008 × 0.0002}}$ is equal to
a) 36
b) 38
c) 34
d) 39
Answer »Answer: (a)
Expression
= $√{{0.009 × 0.036 × 0.016 × 0.08}/{0.002 × 0.0008 × 0.0002}}$
= $√{{9 × 36 × 16 × 8}/{2 × 8 × 2}}$
= 3 × 2 × 3 × 2 = 36
Question : 6
Simplification of ${(3.4567)^2 - (3.4533)^2}/{0.0034}$ yields the result :
a) 7
b) 6.81
c) 6.91
d) 7.1
Answer »Answer: (c)
? = ${(3.4567 + 3.4533)(3.4567 - 3.4533)}/{0.0034}$
= ${6.9100 × 0.0034}/{0.0034}$ = 6.91
Using Rule 8,
${(3.4567 + 3.4533)(3.4567 - 3.4533)}/{0.0034}$
= ${{3.4567}^2 - {3.4533}^2}/{(3.4567 - 3.4533)}$
= 3.4567 + 3.4533 = 6.91
GET simplification PRACTICE TEST 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
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