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Cube and cube roots are fundamental concepts in Class 8 maths. These concepts help us solve problems by finding the cube of a number and the cube root of a number. In this section, we have extra questions on cube and cube roots to help you practice and improve your skills.

These **extra questions Cube and cube roots in Class 8 maths** are designed to be challenging yet manageable, allowing you to develop your critical thinking and problem-solving skills. By working through these questions, you will gain a deeper understanding of the importance of **cube and cube roots class 8 extra questions** in real-life applications and develop a strong foundation for future mathematical studies.

## Extra Questions for Class 8 Maths Chapter 7 Cubes and Cube Roots

Explore the concepts of **extra questions cubes and cube roots for Class 8**. These concepts are crucial for solving various mathematical problems. Here, we have extra questions to help you practice and improve your skills in finding cubes and cube roots.

### Cubes and Cube Roots Class 8 Extra Questions Very Short Answer Type

**Ques: Find the cubes of the following:**

(a) 12

(b) -6

(c) \(\frac { 2 }{ 3 }\)

(d) \(\frac { -5 }{ 6 }\)

**Solution:**

**Ques: Find the cubes of the following:**

(a) 0.3

(b) 0.8

(c) .001

(d) 2 – 0.3

**Solution.**

(a) (0.3)^{3} = 0.3 × 0.3 × 0.3 = 0.027

(b) (0.8)^{3} = 0.8 × 0.8 × 0.8 = 0.512

(c) (0.001)^{3} = (0.001) × (0.001) × (0.001) = 0.000000001

(d) (2 – 0.3)^{3} = (1.7)^{3} = 1.7 × 1.7 × 1.7 = 4.913

Ques: Is 135 a perfect cube?

**Solution:**

Prime factorisation of 135, is:

135 = 3 × 3 × 3 × 5

We find that on making triplet, the number 5 does not make a group of the triplet.

Hence, 135 is not a perfect cube.

**Ques: Find the cube roots of the following:**

(a) 1728

(b) 3375

**Solution:**

**Ques: Examine if (i) 200 (ii) 864 are perfect cubes.**

**Solution:**

**(i) 200 = 2 × 2 × 2 × 5 × 5**

If we form triplet of equal factors, the number 2 forms a group of three whereas 5 does not do it.

Therefore, 200 is not a perfect cube.

**(ii) We have 864 = 2 × 2 × 2 × 2 × 2**

If we form triplet of equal factors, the number 2 and 3 form a group of three whereas another group of 2’s does not do so.

Therefore, 864 is not a perfect cube.

**Ques: Find the smallest number by which 1323 may be multiplied so that the product is a perfect cube.**

**Solution:**

1323 = 3 × 3 × 3 × 7 × 7

Since we required one more 7 to make a triplet of 7.

Therefore 7 is the smallest number by which 1323 may be multiplied to make it a perfect cube.

**Ques: What is the smallest number by which 2916 should be divided so that the quotient is a perfect cube?**

**Solution:**

Prime factorisation of

2916 = 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

Since we required one more 2 to make a triplet

Therefore, the required smallest number by which 2916 should be divided to make it a perfect cube is 2 × 2 = 4, i.e., 2916 ÷ 4 = 729 which is a perfect cube.

**Ques: Check whether 1728 is a perfect cube by using prime factorisation. (NCERT Exemplar)**

**Solution:**

Prime factorisation of 1728 is

1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3

Since all prime factors can be grouped in triplets.

Therefore, 1728 is a perfect cube.

**Ques: Using prime factorisation, find the cube root of 5832. (NCERT Exemplar)**

**Solution:**

**Ques:**

**Solution:**

### Cubes and Cube Roots Class 8 Extra Questions Short Answers Type

**Ques: **

**Solution:**

**Ques: Find the cube roots of**

(i) 4\(\frac { 12 }{ 125 }\)

(ii) -0.729

**Solution:**

**Ques: Express the following numbers as the sum of odd numbers using the given pattern**

**Solution:**

**Ques: Observe the following pattern and complete the blank spaces.**

**1 ^{3} = 1**

**Solution:**