model 1 find largest and smallest value Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 5 EXERCISES
The following question based on power, indices and surds topic of quantitative aptitude
(a) $√^3{4}$
(b) $√2$
(c) $√^6{3}$
(d) $√^4{5}$
The correct answers to the above question in:
Answer: (a)
$√2, √^6{3}, √^3{4}, √^4{5}$
LCM of 2, 6, 3, 4 = 12
$√2=√^12{2^6}=√^12{64}$
$√^6{3}=√^12{3^2}=√^12{9}$
$√^3{4}=√^12{4^4}=√^12{256}$
$√^4{5}=√^12{5^3}=√^12{125}$
Clearly,
$√^12{9}<√^12{64}<√^12{125}<√^12{256}$
∴ $√^6{3}<√2<√^4{5}<√^3{4}$
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Read more largest and smallest value Based Quantitative Aptitude Questions and Answers
Question : 1
The least one of $2√3, 2√^4{5}, √8$ and $3√2$ is
a) $√8$
b) $2√3$
c) $2√^4{5}$
d) $3√2$
Answer »Answer: (a)
$2√3, 2√^4{5}, √8$ and $3√2$
The orders of the surds are 2, 4, 2 and 2. Their LCM = 4
We convert each surd into a surd of order 4.
$2√3=√{4×3}=√12=√^4(12)^2=√^4{144}$
$2√^4{5}=√^4{2^4×5}=√^4{80}$
$3√2=√18=√^4(18)^2=√^4{324}$
$√8=√^4{64}$
Hence, the least number =$√8$
Question : 2
The greatest of the numbers $(2.89)^{0.5}, 2 - (0.5)^2, 1 + {0.5}/{1 - 1/2}, √3$ is :
a) $1 + {0.5}/{1 - 1/2}$
b) $(2.89)^{0.5}$
c) 2 - $(0.5)^2$
d) $√3$
Answer »Answer: (a)
$(2.89)^{0.5}, 2 - (0.5)^2, 1 + {0.5}/{1 - 1/2}, √3$
$(2.89)^{0.5}=(2.89)^{5/10}$
=$√{2.89}=1.7$
=$2 - (0.5)^2=2-0.25=1.75$
$1+{0.5}/{1-1/2}=1+{0.5}/{1/2}$
=$1+{0.5}/{0.5}=1+1=2$
$√3$ =1.732
Question : 3
The greatest among the numbers $√^4{3}, √^5{4}, √^10{12}$, 1 is
a) $√^4{3}$
b) 1
c) $√^5{4}$
d) $√^10{12}$
Answer »Answer: (c)
$√^4{3}, √^5{4}, √^10{12}$, 1
LCM of indices of surds = 20
$√^4{3}=√^20{3^5}=√^20{243}$
$√^5{4}=√^20{4^4}=√^20{256}$
$√^10{12}=√^20{144}$
Question : 4
The largest among the numbers 0.9, $(0.9)^2, √{0.9}, 0.\ov{9}$ is :
a) $√{0.9}$
b) 0.9
c) $(0.9)^2$
d) 0.$\ov9$
Answer »Answer: (d)
0.9, $(0.9)^2, √{0.9}, 0.\ov{9}$
$(0.9)^2$ = 0.81;
$√{0.9}$ = 0.95
$0.\ov{9} = 9/9 = 1$
Question : 5
The greatest among $√7-√5, √5-√3, √9-√7, √{11}-√9$ is
a) $√9-√7$
b) $√7-√5$
c) $√5-√3$
d) $√{11}-√9$
Answer »Answer: (c)
$√7-√5, √5-√3, √9-√7, √{11}-√9$
$1/{√7-√5}={√7+√5}/{(√7-√5)(√7+√5)}$
=${√7+√5}/{7-5}={√7+√5}/2$,
$1/{√5-√3}={√5+√3}/{(√5-√3)(√5+√3)}$
=${√5+√3}/{5-3}={√5+√3}/2$
Similarly,
$1/{√9-√7}={√9+√7}/2$
$1/{√{11}-√9}={√{11}+√9}/2$
Clearly,${√5+√3}/2$ is the smallest.
$1/{√5-√3}$ is the smallest.
∴ $√5-√3$ is the greatest.
Question : 6
The largest number among $√2, √^3{3}, √^4{4}$ is
a) $√^4{4}$
b) $√2$
c) $√^3{3}$
d) All are equal
Answer »Answer: (c)
$√2, √^3{3}, √^4{4}$
LCM of power of surds = 12
$√2=(2)^{1/2}=(2^6)^{1/12}$
=$√^12{2^6}=√^12{64}$
$√^3{3}=√^12{3^4}=√^12{81}$
$√^4{4}=√^12{4^3}=√^12{64}$
Since 81 is the largest, hence,
$√^3{3}$ is the largest number.
GET power, indices and surds PRACTICE TEST EXERCISES
model 1 find largest and smallest value
model 2 based on simplification
model 3 based on positive and negative exponent
model 4 simplifying roots with values
model 5 simplifying roots of roots
power, indices and surds Shortcuts and Techniques with Examples
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model 1 find largest and smallest value
Defination & Shortcuts … -
model 2 based on simplification
Defination & Shortcuts … -
model 3 based on positive and negative exponent
Defination & Shortcuts … -
model 4 simplifying roots with values
Defination & Shortcuts … -
model 5 simplifying roots of roots
Defination & Shortcuts …
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