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

Question : 16 [SSC SAS 2010]

The least number, that must be added to 1720 so as to obtain a perfect cube, is

a) 13

b) 7

c) 11

d) 8

Answer: (d)

12 × 12 × 12 = 1728

∴ Required number

= 1728 - 1720 = 8

Question : 17

The value of $√{√^3{0.000729}}$ is

a) 0.09

b) 0.9

c) 0.03

d) 0.3

Answer: (d)

Expression

= $√{√^3{0.000729}}$

= $√{√^3{0.09 × 0.09 × 0.09}}$

= $√{0.09} = √{0.3 × 0.3}$ = 0.3

Question : 18 [SSC CGL Prelim 2003]

Sum of digits of the smallest number by which 1440 be multiplied so that it becomes a perfect cube, is

a) 8

b) 4

c) 7

d) 6

Answer: (d)

1440 = $2 × 2 × 2 × 2 × 2 × 3 × 3 × 5 = 2^3 × 2^2 × 3^2 × 5$

To make 1440 a perfect cube, it must be mulitplied by 2 × 3 × 5 × 5 = 150.

∴The required sum = 1+5 + 0 = 6

Question : 19 [SSC CGL Tier-1 2011]

$√^3{1 - {127/343}}$ is equal to

a) 1 - $2/7$

b) $5/9$

c) $4/7$

d) 1 - $1/7$

Answer: (d)

Expression

= $√^3{1 - 127/343} = √^3{{343 - 127}/343}$

= $√^3{216/343} = √^3{(6)^3/(7)^3}$

= $6/7 = 1 - 1/7$

Question : 20 [SSC CPO S.I.2007]

The smallest positive integer n, for which 864n is a perfect cube, is :

a) 4

b) 1

c) 3

d) 2

Answer: (d)

2864
2432
2216
2108
254
327
39
3
864 = $2^3 × 3^3 × 2^2$

For 864n to be a perfect cube, n = 2

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