Model 1 Find Largest And Smallest Value Practice Questions Answers Test With Solutions & More Shortcuts
POWER, INDICES AND SURDS PRACTICE TEST [5 - 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
Question : 11 [SSC CPO S.I.2003]
The greatest one of $√2, √^3{3}, √^6{6}, √^5{5}$ is
a) $√^6{6}$
b) $√2$
c) $√^3{3}$
d) $√^5{5}$
Answer »Answer: (c)
$√2, √^3{3}, √^6{6}, √^5{5}$
LCM of 2, 3, 6 & 5 = 30
$2^{1/2} = 2^{15/30} = √^30{2^15}=32768$
$3^{1/3} = 3^{10/30} = √^30{3^10}= 59049$
$6^{1/6} = 6^{5/30} = √^30{6^5}=7776$
$5^{1/5} = 5^{6/30} = √^30{5^5}$= 15625
Therefore, $√^3{3}$ is the greatest.
Question : 12
The greatest number among $√^3{2}, √3, √^3{5}$ and 1.5 is :
a) $√3$
b) $ √^3{2}$
c) $√^3{5}$
d) 1.5
Answer »Answer: (a)
$√^3{2}, √3, √^3{5}$ and 1.5
LCM of 3 and 2 = 6.
$√^3{2}=√^6{2^2}=√^6{4}$
$√3=√^6{27}$
$√^3{5}=√^6{25}$
1.5 =$√{2.25}=√^6{(2.225)^3}$
Question : 13 [SSC CGL Prelim 2005]
Which is the greatest among $(√{19} - √{17}),(√{13} -√{11}),(√7 -√5)$ and $(√5-√3)$ ?
a) $√7 -√5$
b) $√{19} - √{17}$
c) $√{13} -√{11}$
d) $√5-√3$
Answer »Answer: (d)
$(√{19} - √{17}),(√{13} -√{11}),(√7 -√5)$ and $(√5-√3)$
$√{19} - √{17}$
=${(√19-√17)×(√19+√17)}/{√19+√17}$
${19-17}/{√19+√17}=2/{√19+√17}$
Similarly,$√{13} -√{11}=2/{√{13} +√{11}}$
$√7 -√5=2/{√7 +√5}$
$√5-√3=2/{√5+√3}$
Clearly, $√5-√3$ is the greatest.
(Smaller the denominator, greater the no.)
Question : 14
Among the numbers $√2, √^3{9}, √^4{16}, √^5{32}$ the greatest one is
a) $√^4{16}$
b) $√2$
c) $√^3{9}$
d) $√^5{32}$
Answer »Answer: (c)
$√2, √^3{9}, √^4{16}, √^5{32}$
$(16)^{1/4}=(2^4)^{1/4}=2$
$√^5{32}=(32)^{1/5}=(2^5)^{1/5}=2$
$√^3{9}>2,√2<2$
Question : 15 [SSC CPO SI 2016]
Which is the largest among the numbers $√5 , 3√7 , 4√13$
a) 4$√13$
b) $√5$
c) 3$√7$
d) All are equal
Answer »Answer: (a)
$√5 , 3√7 , 4√13$
$√5$
$3√7 =√{9×7}=√63$
$√^4{13}=√{4×4×13}=√{208}$
Clearly,$√5<3√7<4√13$
IMPORTANT QUANTITATIVE APTITUDE EXERCISES
Model 1 Find Largest And Smallest Value Shortcuts »
Click to Read...Model 1 Find Largest And Smallest Value Online Quiz
Click to Start..POWER, INDICES AND SURDS SHORTCUTS AND TECHNIQUES WITH EXAMPLES
-
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 …
QUANTITATIVE APTITUDE CATEGORIES
-
» Number System
-
» Average
-
» LCM & HCF
-
» Percentage
-
» Profit & Loss
-
» Time & Work
-
» Pipes & Cisterns
-
» Time & Distance
-
» Trains
-
» Compound Interest
-
» Simplification
-
» Discount
-
» Power
-
» Permutations & Combination
-
» Ratio & Proportion
-
» Advance Math
-
» Algebraic Expressions
-
» Trigonometric Ratios & Identities
-
» Simple Interest
-
» Alligation & Mixtures
-
» Boats & Streams
-
» Set Theory
-
» Linear Equations
-
» Quadratic Equations
-
» Mensuration
-
» Squareroots & Cuberoots
-
» Data Sufficiency
-
» Logarithm
-
» Probability
-
» Statistics
RECENT BLOGS
Recently Added Subject & Categories For All Competitive Exams
Alphabet and Number Arrangement Aptitude Model Test SSC
Alphabet and Number Arrangement objective Questions with detailed answers, PDF. Aptitude 50+ Practice MCQ exercises for SSC, all competitive, Bank Exams
Continue Reading »
SSC Direction and Distance Sense MCQ Practice Exercise
Top Direction and Distance Sense objective questions with answers, PDF for SSC. 100+ Aptitude practice exercises for all Bank, Govt, and Competitive Exams
Continue Reading »
100+ Blood Relation Aptitude Test Online, PDF for SSC
Top Blood Relation objective questions with answers, download PDF for SSC. 100+ Aptitude online practice exercises for all Bank, Govt, and Competitive Exams
Continue Reading »
Top 100+ English Jumbled Sentences MCQ with PDF for RBI
Very important Jumbled Sentences questions with answers PDF for RBI. 100+ General English practice exercises for all Bank, Govt, and Competitive Exams
Continue Reading »