CBSE Class 8 Maths Worksheet Chapter 7 Cube and Cube Roots - PDF

The Class 8 Maths Cube and Cube Roots worksheet is answered simply and engagingly. The problems from Chapter 7 of the CBSE Class 8 textbook have been thoroughly and step-by-step handled by our experienced team, which helps the students solidify their understanding.

The Class 8 Maths Cube and Cube Roots answer is a comprehensive resource for teachers of students in Class 8. Through the use of these Maths worksheets, educators can gain knowledge and understanding about the development of students as well as methods and techniques for teaching them effectively.

Examples of Class 8 Cube and Cube Roots

Here are some common examples of Cube and Cube Roots exercises:

Q. Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube. 

(a) 243 

Ans: The prime factorization of 243 is

243 = 3 × 3 × 3 × 3 × 3

Here, two 3s are extra, which are not in a triplet. To make 243 a cube, one more 3 is required. 

In that case, 

243 × 3 = 3×3×3×3×3×3 = 729

243 × 3 = 3×3×3×3×3×3 = 729 is a perfect cube. 

Therefore, the smallest natural number by which 243 should be multiplied to make it a perfect cube is 3.

(b) 256 

Ans: The prime factorization of 

256 = 2×2×2×2×2×2×2×2

Here, two 2s are extra, which are not in a triplet. To make 256 a cube, one more is required. Then, we obtain 

256 × 2 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 512

256 × 2 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 512 , which is a perfect cube.

Therefore, 2 is the smallest natural number by which 256 should be multiplied to make it a perfect cube. 

(c) 675

Ans:

675 = 3 × 3 × 3 × 5 × 5

675 = 3 × 3 × 3 × 5 × 5 Here, two 5s are extra, which are not in a triplet. To make 675 a perfect cube, one more 5 is required. 

Then, we obtain 

675 × 5 = 3 × 3 × 3 × 5 × 5 × 5 = 3375

675 × 5 = 3 × 3 × 3 × 5 × 5 × 5 = 3375 (a perfect cube). 

Therefore, 5 is the smallest natural number by which 675 should be multiplied to make it a perfect cube. 

Q. True or False Type Questions.

(i) A perfect cube never ends with two zeroes. 

Answer: True.

Reason: Perfect cube ends with a fixed number of zeroes, always a perfect multiple of 3.

e.g., the cube of 10 is 1000, having three zeroes at the end. The cube of 100 is 1000000, having six zeroes at the end. 

(ii) If a square of any number ends with 5, its cube will always end with 25.

Answer: False. 

Reason: It is not the necessary condition that if any square of a number ends with 5, then its cube will certainly end with 25. 

e.g., the square of 25 =625

625 has its unit digit as 5. 

The cube of 25 is 15,625. 

However, the square of 35 is 1,225 and has its unit place digit as five, but the cube of 35 is 42875, which does not end with 25.

Q. We know that 1,331 is the ideal cube. Can you figure out what its cube root is without factorization? Try to determine the cube roots of 4913, 12167, and 32768.

Solution:

(i) When we combine the digits, we obtain 1 and 331.

Assuming that the unit digit of the cube is 1, we can infer that the unit digit of the cube root is also 1.

We obtain 1 as the cube root of 1331's unit digit.

The number in the second group matches the cube of 1 exactly.

Our cube root's tenth digit is used as the smallest number's unit place.

As we know that the unit digit of a number's cube whose unit location is the number one is 1

∴ \[\sqrt[3]{1331 } \] = 11

(ii) The result of grouping the digits is 4 and 913.

Since the unit digit for the cube is 3, we can infer that the unit digit for the cube root is 7. This gives us 7 as the unit digit for the cube root of 4913. As 1 > 4 > 8, we know that 13 = 1 and 23 = 8.

So, we assume 1 to be the tenth digit of the cube root.

∴ \[ \sqrt[3]{4913} \] = 17

(iii) The results of grouping the numerals are 12 and 167.

As the unit digit of the cube is 7, we know that the unit digit of the cube root is 3.

The unit digit of 12167's cube root is 3. Since 8 > 12 > 27, we know that 23 = 8 and 33 = 27.

So, 2 is used as the tenth digit of the cube root.

∴ \[\sqrt[3]{12167}\] = 23

(iv) By grouping the digits, we will get 32, 768.

As We know, the unit digit of the cube = 8,

 and the unit digit of the cube root = 2.

Therefore, 2 is the unit digit of the cube root of 32768. We know 3³ = 27 and 4³ = 64 , 27 > 32 > 64.

Thus, 3 is taken as ten digits of cube root.

∴ \[\sqrt[3]{32768} \] = 32

What Does Class 8 Maths Worksheet Chapter 7 PDF Consist?

Students can find a reliable Cube and Cube root Class 8 Maths PDF on the main website of Vedantu. There are answers to every question in the textbook in both the PDF file and the latest worksheet to practice for exams. Students can download the free Cube and Cube and Cube roots lesson worksheet for class 8 on any device with a stable internet connection. Designed by client experts to meet students' individual needs, these Maths worksheets offer the highest quality of education.

• Cube root exercises have been well-formulated following the latest CBSE guidelines.

• Provides various exercises with examples for cube root sums for class 8, finding perfect cubes, etc.

• Solving MCQ on cubes and cube roots will help children grasp concepts quickly.

• For parents, these Maths cubes and cube roots worksheets for class 8 offer an easy way to monitor their children's progress.

Students can find Vedantu's Cubes And Cube Roots Class 8 PDF about the difference between cubes and cube roots with a fun and easy explanation. Cubes and Cube Roots worksheets for Class 8 with answers also explain to the students how to use the prime factorization method to determine an integer's cubes and cube roots. The process for determining a cube number's cube root is also covered in this chapter with cubes and cubes roots for integers with no more than three digits after completing the chapter "Cubes and Cube Roots."