Model 3 Simplification Based On Cube & Cube Root Practice Questions Answers Test With Solutions & More Shortcuts

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: (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: (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: (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: (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: (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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