Model 3 Simplification based on cube & cube root Practice Questions Answers Test with Solutions & More Shortcuts

Question : 11 [SSC CPO S.I.2004]

The sum of the cubes of the numbers 22, –15 and –7 is equal to

a) 0

b) 6930

c) 3

d) 9630

Answer: (b)

Here, 22 - 15 - 7 = 0

We know that

$a^3 + b^3 + c^3$ = 3abc,

if a + b + c = 0

$(22)^3 + (–15)^3 + (–7)^3$

= 3 × 22 × (–15) (–7) = 6930

Question : 12 [SSC CGL Prelim 2000]

The square of a natural number subtracted from its cube is 48. The number is :

a) 4

b) 8

c) 5

d) 6

Answer: (a)

Let number be x

According to question,

$x^3 - x^2$ = 48 ⇒ ∴ x = 4

Question : 13 [SSC Investigator 2010]

$√^3{0.000125}$ is equal to

a) 0.005

b) 0.5

c) 0.05

d) 0.15

Answer: (c)

$√^3{0.000125} = √^3{0.05 × 0.05 × 0.05}$

= 0.05

Question : 14 [SSC CGL Prelim 2002]

If cube root of 175616 is 56, then the value of $√^3{175.616} + √^3{0.175616} + √^3{0.000175616}$ is equal to :

a) 6.116

b) 0.168

c) 6.216

d) 62.16

Answer: (c)

Here, $√^3{175616}$ = 56

$√^3{175.616}$ = 5.6

$√^3{0.175616}$ = 0.56

and $√^3{0.000175616}$ = 0.056

Required sum

= 5.6 + 0.56 + 0.056 = 6.216

Question : 15 [SSC CPO S.I.2010]

$(√^3{1000} + √^3{0.008} - √^3{0.125})$ is equal to

a) 9.9997

b) 9.7

c) 9.997

d) 9.97

Answer: (b)

$√^3{1000} + √^3{0.008} - √^3{0.125}$

= 10 + 0.2 - 0.5 = 9.7

IMPORTANT quantitative aptitude EXERCISES

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