Model 3 Simplification Based On Cube & Cube Root Practice Questions Answers Test With Solutions & More Shortcuts
SIMPLIFICATION PRACTICE TEST [4 - EXERCISES]
Model 1 Simplification Using VBODMAS
Model 2 Simplification Based On Square & Square Root
Model 3 Simplification Based On Cube & Cube Root
Model 4 Simplification With Continued Fraction
Question : 6
$√^3{8}/√{16} ÷ √{100/49} × √^3{125}$ is equal to :
a) $4/7$
b) 7
c) $7/100$
d) 1$3/4$
Answer »Answer: (d)
On simplification,
Expression = $2/4 × 7/10 × 5$
= $7/4 = 1{3}/4$
Question : 7 [SSC CGL Prelim 2000]
$√^3{{72.9}/{0.4096}}$ is equal to :
a) 13.6
b) 0.5625
c) 182
d) 5.625
Answer »Answer: (d)
$√^3{{72.9}/{0.4096}} = √^3{{729000}/{4096}}$
= $√^3{(90)^3/(16)^3} = 90/16 = 45/8 = 5.625$
Question : 8 [SSC CGL Prelim 2007]
The sum of the squares of 2 numbers is 146 and the square root of one of them is $√5$. The cube of the other number is
a) 1441
b) 1111
c) 1331
d) 1221
Answer »Answer: (c)
First number = $(√5)^2 = 5$
Let the second number be x.
$x^2 + 5^2 = 146$
$x^2$ = 146 –25 = 121
$x = √{121} = 11$
Cube of 11 =1331
Question : 9 [SSC CPO S.I.2010]
By what least number should 4320 be multiplied so as to obtain a number which is a perfect cube ?
a) 80
b) 40
c) 60
d) 50
Answer »Answer: (d)
4320 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5
= $2^3 × 3^3 × 2^2 × 5$
Required number = 2 × 5 × 5 = 50
Question : 10
Which of the following is a perfect square as well as a cube? 343, 125, 81, or 64
a) 64
b) 81
c) 343
d) 125
Answer »Answer: (a)
343 = 7 × 7 × 7
125 = 5 × 5 × 5
81 = 3 × 3 × 3 × 3
64 = 8 × 8 = 4 × 4 × 4
We see that 343 and 125 are only perfect cubes of 7 and 5 respectively.
81 is only a perfect square of 9. 64 is a perfect square of 8 as well as a perfect cube of 4.
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