# Free Cubes and Cube Roots 03 Practice Test - 8th Grade

### Question 1

What is the units digit of the cube of the number whose unit digit is 7?

3

5

4

2

#### SOLUTION

Solution :A

The units digit of the cube of 7 i.e.343 is 3.

Thus, the units digit of the cube of the number whose unit digit is 7 will be 3.

### Question 2

What is the value of 3√−8−3√−216 ?

4

-8

-4

8

#### SOLUTION

Solution :A

- 8 = - 2×−2×−2

3√−8 = −2

- 216 = −6×−6×−6

3√−216 = −6

So the given expression 3√−8−3√−216 becomes - 2 - (- 6) = - 2 + 6

= 4

### Question 3

What should be multiplied to 43200 to make it a perfect cube?

2

3

5

Already a perfect cube

#### SOLUTION

Solution :C

For a number to be a perfect cube, its prime factors should be in the form of triplets

By prime factorization, 43200 = 26× 33× 52Only two 5’s are there so we need one more 5 to make a triplet.

So if 43200 is multiplied by 5, we get a perfect cube.

### Question 4

Which of the following could be the cube of 37?

50653

50666

50892

55018

#### SOLUTION

Solution :A

The cube of an odd number is odd. So only 50653 is possible. We can also check the answer by calculating the cube of 37

= 37 × 37 × 37 = 50653.

### Question 5

Which of these is not a perfect cube?

343

1331

512

81

#### SOLUTION

Solution :D

By prime factorization, we have

343=7×7×71331=11×11×11 512=8×8×8 81=3×3×3×3

For a number to be a perfect cube ,each of its factors must be repeated thrice.

343, 1331 and 512 are the perfect cubes of 7, 11 and 8 respectively, whereas 81 is not, as 3 is repeating 4 times which is not a triplet.81 is not a perfect cube.

### Question 6

With what number should 1715 be divided to get a perfect cube?

1

7

5

Already a perfect cube

#### SOLUTION

Solution :C

For a number to be a perfect cube, its prime factors should be expressed as triplets

By prime factorization, we get 1715 = 7×7×7×5We have three 7’s but only one 5 so we need to divide the number by 5.

### Question 7

100 is the smallest square number that is the sum of cubes of 4 consecutive natural numbers.

True

False

#### SOLUTION

Solution :A

100 = 102

= 13+ 23+ 33+ 43

= 1+8+27+64

### Question 8

Anshul and Balendu have 50 cubes of side 1 cm. They decided to make a larger cube by joining these smaller cubes. The number of larger cubes (all of different sizes) they can make is

#### SOLUTION

Solution :Since the side of the smaller cube is 1 cm, its volume will be 1 cubic cm.

We know that the volume of cubes of sides 1,2,3,4,... are 1,8,27,64...cubic cm.

But Anshul and Balendu have only 50 small cubes, so they can make cubes of 3 sizes with the help of 1,8 and 27 smaller cubes.

It should be noted that (50-1-8-27) = 14 smaller cubes will be left unused.

### Question 9

The cube of a number is less than its square in which of the following cases ?

The number lies between -1 and 0

The number is 0

#### SOLUTION

Solution :A and C

Cube of a negative number is negative but square of a negative number is positive. Thus, for a number lying between -1 and 0, the cube is less than its square.

The cube as well as the square of 0 is zero. For decimal numbers less than 1, the cube of a number is lesser than its square. For a number greater than 1, its cube is greater than its square.

### Question 10

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

True

False

#### SOLUTION

Solution :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.