Cubes and Cube Roots Test

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Cubes and Cube Roots Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following is the smallest number that must be multiplied with 4500 to form a perfect cube?

A
2

B
3

C
6

D
8

Solution

4500 = 2 2 3 3 5 5 5
The factors have three 5's, only two 2's and two 3's.
So, to make triplets of 2's and 3's, we need one 2 and one 3 more.
So, to make a perfect cube, we should multiply the given number by 2 3 = 6.
Question 2
1 / -0

Anuj wants to make a cube. He has a cuboid of dimensions 3 cm 2 cm 3 cm. How many such cuboids will he need to form a cube?

A
12

B
20

C
6

D
24

Solution

To make triplets, he needs 3 2 2 = 12 cuboids.
So, 12 cuboids are needed.
Question 3
1 / -0

Which of the following statements is/are true?

(i) 6 should be multiplied with 182 to make it a perfect cube.
(ii) 5 should be multiplied with 235 to make it a perfect cube.

A
Both (i) and (ii) are true.

B
Only (i) is true.

C
Only (ii) is true.

D
Both (i) and (ii) are false.

Solution

(i) 182 = 2 13 7
To make it a perfect cube, we don't need 6.
(ii) 235 = 5 47
To make it a perfect cube, we need two 5s and two 47s.
Hence, both (i) and (ii) are false.
Question 4
1 / -0

Which of the following is true?

A
2²3³13³ must be divided by 2 to make the quotient a perfect cube.

B
2² 3³13³ must be multiplied by 2² to make the product a perfect cube.

C
2 must be multiplied by the factors of 2744 to make it a perfect cube.

D
2²3²13³17³ must be divided by 36 to make the quotient a perfect cube.

Solution

2²3²13³17³
As 2 and 3 are not grouped in triplets, so it must be divided by 2²3² = 36 to make quotient a perfect cube.
Question 5
1 / -0

Where A, B, C and D are prime numbers and are arranged in ascending order. Then which of the following is true?

A
A < B

B
A = B = C

C
A = B

D
C = D

Solution

A = 2, B = 2, C = 3 and D = 11
A = B
Question 6
1 / -0

A teacher wrote a perfect cube number on the board. A student copied it on his notebook and by mistake he forgot to copy 2 digits and wrote the number as 140AB8. The teacher asked to find the sum of digits of the cube root of the number. What was the sum?

A
5

B
7

C
2

D
9

Solution

140 AB8
Step 1: Take a group as AB8.
Last digit is 8 or
So, units digit of cube root of the number is 2.
Step 2: Take another group 140.
125 < 140 < 216
Step 3: Take the smallest cube-root which is 5 in this case.
So, tens place of the number is 5.
Cube root of number = 52
Sum of digits of the cube root of the number = 5 + 2 = 7.
Question 7
1 / -0

What is the unit digit of (23173)³ + (743129)³?

A
9

B
7

C
2

D
6

Solution

Unit digit of (23173)³ = Unit digit of 3³ = 7
Unit digit of (743129)³ = Unit digit of 9³ = 9
Adding unit digits,
7 + 9 = 16
The unit digit of (23173)³ + (743129)³= 6
Question 8
1 / -0

The cube of an even natural number is always

A
even

B
odd

C
even or odd

D
can't say

Solution

The cube of an even natural number is always even.
For example:
Cube of 2 = 2 × 2 × 2 = 8
Cube of 4 = 4 × 4 × 4 = 64
Cube of 6 = 6 × 6 × 6 = 216 and so on.
Question 9
1 / -0

Which of the following is the smallest perfect odd cube between 1700 to 5000?

A
1727

B
2197

C
1731

D
4913

Solution

12³ = 1728
13³ = 2197
14³ = 2744
15³ = 3375
16³ = 4096
17³ = 4913
Question 10
1 / -0

Three numbers are in the ratio 1 : 2 : 3. If the sum of their cubes is 12348, what are the numbers?

A
7, 14, 21

B
8, 16, 24

C
9, 18, 27

D
6, 12, 18

Solution

Let numbers be x, 2x and 3x.
Their cubes = x³, 8x³, 27x³
According to question
x³ + 8x³ + 27x³ = 12348
36x³ = 12348 x³ = = 343 = (7)³
So, x = 7
Numbers = 7 1 = 7, 7 2 = 14, 7 3 = 21
7, 14, 21
Question 11
1 / -0

What is the smallest number by which 3087 must be divided so that the quotient obtained is a perfect cube?

A
6

B
9

C
11

D
12

Solution

3087 = 7 × 7 × 7 × 9
To obtain a perfect cube, we need to divide 3087 by 9.
So, the correct answer is 9.
Question 12
1 / -0

Which of the following numbers is the same as ?

A
1

B
3

C
5

D
7

Solution

= 3
Question 13
1 / -0

Which of the following numbers is the same as ?

A
3

B
9

C
10

D
15

Solution

=
= 9
Question 14
1 / -0

What is the sum of and ?

A
58

B
48

C
42

D
40

Solution

+ = (19 x 2) + (4 - 2)
= 38 + 2 = 40
Question 15
1 / -0

The cube root of a number 'x' is 5 more than the 4^th multiple of 5. What is the cube root of a number 'y' such that 'y' is 8764 more than 'x'?

A
33

B
31

C
29

D
27

Solution

= 5 + (4 x 5)
= 5 + 20 = 25
x = (25)³ = 15625
y = 8764 + 15625 = 24389
(y)^1/3 = (24389)^1/3 = (29 x 29 x 29)^1/3 = 29