Cubes And Cube Roots(8th Grade > Mathematics ) Questions and answers for exam Preparation

Question 1. Which of the following could be the cube of 37?

50653
50666
50892
55018

Explanation:-

Answer: Option A. -> 50653
:
A
The cube of an odd number is odd. Soonly 50653 is possible. We can alsocheck the answer bycalculatingthe cube of 37
= 37

\times

37

\times

37 = 50653.

Question 2. The cube of average of 3 and 7 will also be the average of the of the cubes of 3 and 7.

True
False
The number lies between 0 and 1
The number lies between 1 and 2

Explanation:-

Answer: Option B. -> False
:
B
The average of 3 and 7 is 5. The cube of 5 is 125.The cube of 3 and 7 is 27 and 343 respectively. The average of 27 and 343 is 185 which is not the cube of 5.

Question 3. What is the value of

\sqrt[3]{- 8} - \sqrt[3]{- 216}

?

4
-8
-4
8

Explanation:-

Answer: Option A. -> 4
:
A
- 8 = -

2 \times - 2 \times - 2

\sqrt[3]{- 8} = - 2

- 216 =

- 6 \times - 6 \times - 6

\sqrt[3]{- 216} = - 6

So the given expression

\sqrt[3]{- 8} - \sqrt[3]{- 216}

becomes - 2 - (- 6) = - 2 + 6
= 4

Question 4. The cube root of 30 lies between 5 and 6.

True
False
4
5

Explanation:-

Answer: Option B. -> False
:
B
The cube of 3 = 27
The cube of 4 = 64
Since 30 lies between 27 & 64 so its cube root must lie between 3 & 4.
Hence, the given statement is false.

Question 5. The digit in the units place in the cube of 298 is

2
3
8
4

Explanation:-

Answer: Option A. -> 2
:
A
The digit in the units place in 298 is 8.
cube of 8 is 512, which ends in 2.
Hence, the digit in the units place in the cube of 298 is 2

Question 6.

a^{3}

-

b^{3}

is always divisible by:

a - b
a × b
a + b
2a + b

Explanation:-

Answer: Option A. -> a - b
:
A
Take

a = 2

and

b = 1

and check.
Alternatively, we know the algebraic identity,

a^{3} - b^{3} = (a - b) (a^{2} + 2 a b + b^{2}

)
Hence , we can see that

(a - b)

is a factor of

a^{3}

-

b^{3}

Thus,

a^{3}

-

b^{3}

is divisible by

(a - b)

Question 7. The number of students in class 20 minutes ago was 729 . If the number of students joining the class triples every 10 minutes, what is the cube root of the number of students joining after 40 minutes from now?

81
27
64
48

Explanation:-

Answer: Option A. -> 81
:
A
For every 10 mins passage of time, the number of students joining the class gets tripled i.e. multiplied by 3
The number of students joining after 40 minutes from now on is

729 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3

( from 20 mins back to 40 mins forward)
The cube root of 729 is 9.
Cube root of given number is

9 \times 3 \times 3 = 81

Question 8. What is the sum of the cubes of the first 7 natural numbers?

784
774
441
788

Explanation:-

Answer: Option A. -> 784
:
A
Sum of cubes of first n natural numbers is

\frac{(n (n + 1))^{2}}{4}

Putting n = 7,

\frac{(7 (7 + 1))^{2}}{4}

\frac{(7 \times 8)^{2}}{4}

= 784.

Question 9. What is the minimum number that should be multiplied with 360 in order to make it a perfect cube ?

75
70
65
80

Explanation:-

Answer: Option A. -> 75
:
A
For a number to be a perfect cube, its prime factors should be in the form of triplets i.e. every prime factor should be raised to the power in multiples of 3
Prime factorizing the given number, we get

360 = 2 \times 2 \times 2 \times 3 \times 3 \times 5

Hence, we can see that the given number must be multiplied by

3 \times 5 \times 5

i.e.75

Question 10. Which of the following is a perfect cube?

532
729
827
943

Explanation:-

Answer: Option B. -> 729
:
B
By prime factorization,we get 729 =

3 \times 3 \times 3 \times 3 \times 3 \times 3 = 3^{6}

So cube root of

729 = (729)^{\frac{1}{3}} = 3^{\frac{6}{3}} = 3^{2} = 9

Since, the cube root of 729 is a natural number, 729 is a perfect cube.