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) 36.304
(b) 37.304
(c) 36.164
(d) 37.164
The correct answers to the above question in:
Answer: (b)
$√{1.3} + √{1300} + √0.013$
= $√{{130}/{100}} +10√{13} + √{{130}/{10000}}$
= $1/10√{130} + 10√{13} + 1/100√{130}$
= ${11.40}/10 + 3.605 × 10 + {11.40}/100$
= 1.140 + 36.05 + 0.1140
= 37.304
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Read more problems based on squares and roots Based Quantitative Aptitude Questions and Answers
Question : 1
$√{{0.081 × 0.484}/{0.0064 × 6.25}}$ is equal to
a) 0.9
b) 99
c) 9
d) 0.99
Answer »Answer: (d)
Expression
=$√{{0.081 × 0.484}/{0.0064 × 6.25}}$
= $√{{81 × 484}/{64 × 625}} = {9 × 22}/{8 × 25} = 0.99$
Question : 2
The square root of ${0.342 × 0.684}/{0.000342 × 0.000171}$ is :
a) 2500
b) 2000
c) 250
d) 4000
Answer »Answer: (b)
$√{{0.342 × 0.684}/{0.000342 × 0.000171}}$
= $√{{342 × 684 × {10}^6}/{342 × 171}}$
= $√{4 × {10}^6} = 2 × {10}^3$ = 2000
Question : 3
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 »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 : 4
The value of $(3 + √{8}) + 1/{3 - √{8}} - (6 + 4√{2})$ is
a) 1
b) $√2$
c) 8
d) 0
Answer »Answer: (d)
${1/{3 - √8}} = {3 + √8}/{(3 - √8)(3 + √8)}$
(Rationalising the denominator)
= ${3 + √8}/{9 - 8} = 3 + √8$
Expression
= $3 + √{8} + 3 + √{8} - 6 - 4√{2}$
= $6 + 2√{8} - 6 - 4√{2} = 2√{8} - 4√{2}$
= $2 × 2√{2} - 4√{2} = 0$
Question : 5
The value of $√{5+ √{11 + √{19 + √{29 + √{49}}}}}$ is
a) 9
b) 7
c) 3
d) 5
Answer »Answer: (c)
$√{5+ √{11 + √{19 + √{29 + √{49}}}}}$
$√{5+ √{11 + √{19 + √{29 + 7}}}}$
$√{5+ √{11 + √{19 + 6}}}$
$√{5+ √{11 + √{25}}}$
$√{5+ √{11 + 5}}$
$√{5+ 4} = √9$ = 3
Question : 6
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
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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