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 : 31 [SSC CHSL 2013]
Out of the numbers 0.3, 0.03, 0.9, 0.09 the number that is nearest to the value of $√{0.9}$ is
a) 0.9
b) 0.3
c) 0.03
d) 0.09
Answer »Answer: (a)
Question : 32 [SSC CGL Tier-I 2014]
Arranging the following in descending order, we get $√^3{4}, √2, √^6{3}, √^4{5}$
a) $√2>√^6{3}>√^3{4}>√^4{5}$
b) $√^3{4}>√^4{5}>√2>√^6{3}$
c) $√^4{5}>√^3{4}>√^6{3}>√2$
d) $√^6{3}>√^4{5}>√^3{4}>√2$
Answer »Answer: (b)
$√^3{4}, √2, √^6{3}, √^4{5}$
LCM of indices = LCM of 3,6, 4 and 2 = 12
$√^3{4}=(4)^{1/3}=(4)^{1/12}=√^12{4^4}=√^12{256}$
$√2=(2)^{1/2}=√^12{2^6}=√^12{64}$
$√^6{3}=√^12{3^2}=√^12{9}$
$√^4{5}=√^12{5^3}=√^12{125}$
Clearly,$√^3{4}>√^4{5}>√2>√^6{3}$
Question : 33 [SSC CGL Prelim 2008]
Which of the following is the largest number ? $√2, √^3{3}, √^4{4}, √^6{6}$
a) $√^4{4}$
b) $√2$
c) $√^3{3}$
d) $√^6{6}$
Answer »Answer: (c)
$√2, √^3{3}, √^4{4}, √^6{6}$
LCM of 2, 3, 4 and 6 = 12
$√2 =(2)^{1/2} =(2)^{6/12}$
$= (2^6)^{1/12}=√^12{2^6}=√^12{64}$
$√^3{3}=√^12{3^4}=√^12{81}$
$√^4{4}=√^12{4^4}=√^12{64}$
$√^6{6}=√^12{6^2}=√^12{36}$
Question : 34 [SSC CGL Prelim 1999]
Which one of the following is the least? $√3, √^3{2}, √2$ and $√^3{4}$
a) $√3$
b) $√2$
c) $√^3{4}$
d) $√^3{2}$
Answer »Answer: (d)
$√3, √^3{2}, √2$ and $√^3{4}$
LCM of 2 and 3 = 6
$√3 = (3)^{1/2}=3^{3/6}=(3^3)^{1/6}=√^6{27}$
$√^3{2} = √^6{2^2} =√^6{4}$
$√{2} = √^6{2^3} =√^6{8}$
$√^3{4} = √^6{4^2} =√^6{16}$
Question : 35 [SSC CHSL 2014]
The greatest number among the following is $4/9, √ {9/49}, 0.47↖{..}, (0.7)^2$
a) $0.47↖{..}$
b) $4/9$
c) $√{9/49}$
d) $(0.7)^2$
Answer »Answer: (d)
$4/9, √ {9/49}, 0.47, (0.7)^2$
Decimal equivalents of fractions :
$4/9=0.44; √{9/49}=3/7=0.43;$
$(0.7)^2=0.49$
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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