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 : 16
Which of the following is the biggest ? $√^3{4}, √^4{6}, √^6{15}$ and $√^12{245}$
a) $√^6{15}$
b) $√^3{4}$
c) $√^4{6}$
d) $√^12{245}$
Answer »Answer: (b)
$√^3{4}, √^4{6}, √^6{15}$ and $√^12{245}$
$√^3{4} =√^12{256}, √^4{6}= √^12{216}$,
$√^6{15} =√^12{225}, √^12{245}$
Question : 17 [SSC CGL Prelim 2007]
Greatest among the numbers $√^3{9}, √3, √^4{16}, √^6{80}$ is
a) $√^4{16}$
b) $√^3{9}$
c) $√3$
d) $√^6{80}$
Answer »Answer: (b)
The orders of the given surds are 3, 2, 4 and 6.
Their LCM = 12
Now we convert each surd into a surd of order 12.
$√^3{9} = (9)^{1/3} =(9)^{4/12} = (9^4)^{1/12}=√^12{6561}$
Similarly,
$√3 =√^12{3^6}=√^12{729}$
$√^4{16} =√^12{16^3}=√^12{4096}$
$√^6{80} =√^12{80^2}=√^12{6400}$
Clearly,
$√^12{729}<√^12{4096}<√^12{6400}<√^12{6561}$
∴ $√^3{9}$ is the greatest number.
Question : 18 [SSC CHSL 2011]
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.
Question : 19 [SSC CGL 2007]
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 : 20 [SSC CHSL 2010]
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
$0.\ov{9} = 9/9 = 1$
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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