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QUESTION: 1

A natural number is said to be a perfect cube, if it is the cube of some _________.

Solution:

The answer is __natural number__

The cube of a natural number is always a natural number.

QUESTION: 2

The cube of 23 is ___________

Solution:

23^{3 }= 23×23×23 = 12167

QUESTION: 3

Find the cube of 75.

Solution:

QUESTION: 4

If n = m × m × m = m^{3}, where m is an integer, then n is a perfect cube and the number m is called the __________ of n.

Solution:

QUESTION: 5

If (2744)^{1/3 }= 2p+2, then the value of P is

Solution:

QUESTION: 6

The cube root of 13824 is __________.

Solution:

By prime factorisation:

13824 is (2x2x2)x(2x2x2)x(2x2x2)x(3x3x3)

Making pairs of three three numbers

which gives 2x2x2x3=24

Therefore cube root of 13824 is 24

QUESTION: 7

The square of a natural number subtracts from its cube comes 100. The number is __________.

Solution:

QUESTION: 8

Find the cube root of 0.001331.

Solution:

QUESTION: 9

Find the smallest number by which 54 must be multiplied so that the product is a perfect cube.

Solution:

QUESTION: 10

Find the ones digit of cube root of 2197.

Solution:

The answer is 3

2197

Unit's place of 2197 = 7

The ones digit of cube root of 2197 will be 3 as 3^{3 }= 27 which has 7 as unit's place

QUESTION: 11

Find the cube root of -5832.

Solution:

QUESTION: 12

The cube root of the 216 x (−32) x 54 is ________

Solution:

We have 216 x (-32) x 54.

Applying prime factorisation gives

which gives -(6 x 2 x 2 x 3)= -72.

QUESTION: 13

If x is ones digit and y is tens digit of a two digit number, then the cube of the number will be _________.

Solution:

QUESTION: 14

If 72×K is a perfect cube, find the value of K.

Solution:

72 = 2×2×2×3×3

If K = 3, 72×K = 72 × 3 = 216 = 6^{3}

is a perfect cube.

QUESTION: 15

If (504 + p) is a perfect cube number, whose cube root is p, then p = ______.

Solution:

Dear Student, we know that 8^{3}= 512

So p = 512−504 = 8

QUESTION: 16

23 is a cube root of _________.

Solution:

QUESTION: 17

Find the side of the cubical box whose volume is 474.552 dm^{3}.

Solution:

QUESTION: 18

If volume of cube is 4913cm³ then length of side of cube is

Solution:

QUESTION: 19

Divide 5673375 by the smallest number so that the product is perfect cube.

Solution:

QUESTION: 20

Solution:

Taking cube both the sides,

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