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QUESTION: 1

Which of the following is not a perfect cube ?

Solution:

QUESTION: 2

The cube of 4 is _______________.

Solution:

QUESTION: 3

The value of 5^{3 }is __________.

Solution:

QUESTION: 4

The cube of an even number is always ____________.

Solution:

QUESTION: 5

The cube of an odd number is always __________.

Solution:

QUESTION: 6

Each prime factor appears _________ times in its cube?

Solution:

QUESTION: 7

Which of the following is Hardy-Ramanujan Number ?

Solution:

This story is very famous among mathematicians. 1729 is sometimes called the “Hardy-Ramanujan number”.

There are two ways to say that 1729 is the sum of two cubes. 1x1x1=1; 12x12x12=1728. So 1+1728=1729 But also: 9x9x9=729; 10x10x10=1000. So 729+1000=1729 There are other numbers that can be shown to be the sum of two cubes in more than one way, but 1729 is the smallest of them.

Ramanujan did not actually discover this fact. It was known in 1657 by a Frenchmathematician Bernard Franicle de Bessy.

But it got famous after the ramanujans above conversation.

So it's famously known as Ramanujan Number.

QUESTION: 8

By which smallest natural number 392 must be multiplied so as to make the product a perfect cube ?

Solution:

392 = 2 × 2 × 2 × 7 × 7

Hence the number should be multiplied by 7 to make it a perfect cube.

QUESTION: 9

The smallest natural number by which 243 must be multiplied to make the product a perfect cube is __________.

Solution:

QUESTION: 10

The smallest natural number by which 704 must be divided to obtain a perfect cube is

Solution:

QUESTION: 11

The smallest natural number by which 135 must be divided to obtain a perfect cube is

Solution:

we have 135 = 3 x 3 x 3 x 5

Grouping the prime factors of 135 into triples, we are left over with 5.

∴ 135 is not a perfect cube

Now, [135]divided by5 = [ 3 x 3 x 3 x 5] divided by5

or 27 = 3 x 3 x 3

i.e. 27 is a perfect cube.

Thus, the required smallest number is 5

QUESTION: 12

Which of the following is not a perfect cube ?

Solution:

QUESTION: 13

The expansion of a^{3} is ___________.

Solution:

QUESTION: 14

What will be the unit digit of the cube of a number ending with 2 ?

Solution:

QUESTION: 15

What will be the unit digit of the cube of a number ending with 4 ?

Solution:

QUESTION: 16

What will be the unit digit of the cube of a number ending with 6 ?

Solution:

QUESTION: 17

A cuboid has dimensions 5cm, 2cm, 5cm. How many such cuboid will be needed to form a cube ?

Solution:

Given, sides of a cuboid are 5cm, 2cm and 5cm

Volume of cuboid =5*2*5 = 50 cm3

Let the side of the cube formed with

minimum number of cuboids = x

Hence volume of the cube = x3

Number of cuboids required = n

Hence n*50 = x3

Now, n*50 must be perfect cube

n*50 = n*2*5*5

So, minimum value of n = 2*2*5 = 20

Hence, the number of cuboid will be

needed to form a cube is 20

QUESTION: 18

How many cuboids of dimensions 15cm, 30cm,15cm will be needed to form a cube ?

Solution:

Given cuboids of dimensions 15cm, 30cm ,15cm

LCM(15, 30, 15) = 30

Since 15*2 = 30

30*1 = 30

and 15*2 = 30 {since a cube has all the dimensions are same}

So, the number of cuboids required to form a cube = 2*1*2 = 4

So, by using 4 cuboids, we can form a cube having side 30 cm each.

QUESTION: 19

729 is the value of _______________.

Solution:

QUESTION: 20

Which of the following is a perfect cube ?

Solution:

QUESTION: 21

What is the volume of a cube whose edge is 2cm ?

Solution:
Volume of cube=2×2×2=8

QUESTION: 22

The symbol for cube root is __________.

Solution:

QUESTION: 23

The cube root of 512 is ________.

Solution:

QUESTION: 24

The value of ∛343 is-

Solution:

QUESTION: 25

Which of the following is true for any natural number n?

Solution:

Take any natural number(except 1). This identity would hold for any natural number.

Natural numbers are 1,2,3,4,5____ upto infinity with all positive terms.

QUESTION: 26

If the volume of a cube is 125 cm^{3} then what would be the length of its side?

Solution:

The length of each edge is 5ft

Explanation:

If the edge of a cube is marked as a, then the volume can be calculated as V= a^3, so here given the volume V

we can write, that:a = 3√V = 3√125 = 5

QUESTION: 27

What will be the unit digit of the cube root of a number ends with 8?

Solution:

QUESTION: 28

What will be the unit digit of the cube root of a number ends with 2?

Solution:

QUESTION: 29

What will be the unit digit of the cube root of a number ends with 3?

Solution:

QUESTION: 30

What will be the unit digit of the cube root of a number ends with 7?

Solution:

QUESTION: 31

9 is the cube root of __________.

Solution:

9 is the cube root of 729 because 9 x 9 x 9 = 729

So option B is correct answer.

QUESTION: 32

The number of digits in the cube root of a 6-digit number is _______.

Solution:

As 100^{3 }= 1000000 which is the smallest 3 digit number. So it’s only 2 digit number which is the cube root of a 6 digit number

QUESTION: 33

How many digits will be there in the cube root of 46656 ?

Solution:

QUESTION: 34

How many digits will be there in the cube root of 512 ?

Solution:

QUESTION: 35

What will be the unit digit of ∛15625

Solution:

If we multiply 5 three times we receive 125 where 5 is at the one’s place. So cube which has 5 at one’s place will have a root which have 5 at one’s place

QUESTION: 36

How many zeros will be there in the cube root of 27000?

Solution:

QUESTION: 37

How many zeros will be there in the cube root of 800?

Solution:

Since in cubes the zeros become triple ,for instance 10*10*10=1000, a number with two zeros does not have a cube root.

QUESTION: 38

If 7^{3 }= 343, then ∛343 = _________.

Solution:

QUESTION: 39

If 8^{3 }= 512, then ∛512 = _______

Solution:

8*8*8 =512

QUESTION: 40

What will be the unit digit of ∛216

Solution:

We can find it by Prime Factorization method

³√216 = 2×2×2×3×3×3

= 2 and 3 are making triplets i.e. 2 and 3

= 2×3 = 6 Thus, we can say that 6 i.e option 'B' is correct.

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