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
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Click to Start..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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