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QUESTION: 1

Find the cube root of 75.

Solution:

∛75 = ∛(4.217 x 4.217 x 4.217)

∛75 = 4.21716

QUESTION: 2

What is the cube of double of ‘a’?

Solution:

Double of a here a+a=2a

So cube of (2a)³=8a³

QUESTION: 3

Which of the following is the cube root of 27000?

Solution:

QUESTION: 4

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

Solution:

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

**Example**

8 = 2 x 2 x 2

8 = 2 ^{3}

8 is the perfect cube because it is a cube of 2 which is a natural number.

But 12 is not a perfect cube because it is not a cube of any natural numbers.

QUESTION: 5

36 x K is a perfect cube number, then K = ______

Solution:

6×6=36 and 36×6=216, which is the cube of 6.

QUESTION: 6

Express 6^{3 }as the sum of odd numbers.

Solution:

We know,

⇒ 31 + 33 + 35 + 37 + 39 + 41 = 216

And the cube of 6 is also 216

⇒ 6 × 6 × 6 = 216

QUESTION: 7

Ones digit of cube of a number depends on the ________ of the number.

Solution:

For example, 11*11*11=121*11

Where one’s digit depends on 1,

121*11=1331 where again one’s digit depends on 1.

Hence one’s digit of a perfect cube of a number depends on one’s digit.

QUESTION: 8

The numbers 1, 8, 27... are ____________.

Solution:

1×1×1 =1

2×2×2 = 8

3×3×3 = 27

4×4×4 = 64

5×5×5 = 125

Hence all are cubes

QUESTION: 9

Ones place digit in the cube of 5832 is ______.

Solution:

A number ending with 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 0 then it's **cube** ends with 1 , 8 , 7 , 4 , 5 , 6 , 3 , 2 , 0 respectively

⇒ One's digit of 5832= 2

⇒ Cube of 2=2^{3} = 8

So, the one's digit of cube of 5832=8

QUESTION: 10

Find the prime factorisation of 175616.

Solution:

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