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RS Aggarwal Solutions Class 8 Chapter-4 Cubes and Cube Roots (Ex 4B) Exercise 4.2

Last updated date: 02nd Aug 2024
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RS Aggarwal Solutions Class 8 Chapter-4 Cubes and Cube Roots (Ex 4B) Exercise 4.2 - Free PDF

When a number (x) is multiplied into three, then the result is known as the Cube of that number. Thus, the Cube for the number (x) becomes x3 or x-Cubed. For example, if the given number is 5. We know that 5 × 5 × 5 = 125. Hence, 125 is called the Cube of 5. On the other hand, the Cube Root of a number is also the reverse process of the Cube of a number and is denoted by ∛. Taking the same example, 5 is called the Cube Root of the number 125. In this Chapter, students will learn more about the Cubes and Cube Roots of a number.

What do you understand about a Cube Root?

In Math, the Cube Root is given as, "Cube Root is the number that has to be multiplied three times to get the number." Now, let us look at the Cube Root formula, where y is the Cube Root of x. ∛x = y. The radical sign ∛ is given as a symbol of Cube Root for any number with a small 3 written on the top left of the sign. Another method to write Cube Root is to write 1/3 as the exponent of a number.

Cube Root is an inverse operation of the Cube of a number.

Free PDF download of RS Aggarwal Solutions Class 8 Chapter-4 Cubes and Cube Roots (Ex 4B) Exercise 4.2 solved by Expert Mathematics Teachers on Vedantu.com. All Exercise 4.2 Questions with Solutions for Class 8 RS Aggarwal to help you to revise complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other Engineering entrance exams.

Register Online for Class 8 Science tuition on Vedantu.com to score more marks in CBSE board examination. Vedantu is a platform that provides free CBSE Solutions (NCERT) and other study materials for students. Math Students who are looking for the better solutions ,can download Class 8 Math NCERT Solutions to help you to revise the complete syllabus and score more marks in your examinations.

FAQs on RS Aggarwal Solutions Class 8 Chapter-4 Cubes and Cube Roots (Ex 4B) Exercise 4.2

1. What is the method of finding the Cube Root of a Number according to RS Aggarwal Solutions Class 8 Chapter-4 Cubes and Cube Roots (Ex 4B) Exercise 4?

The Cube Root can be calculated by using the  prime factorization method. In order to find the Cube Root of a number, find the prime factorization of the given number. Then, divide the factors into groups containing three same factors. After that, remove the Cube Root symbol and multiply the factors to get the answer. If there is any factor left that cannot be divided equally into groups of three, that means the given number is not a perfect Cube and we cannot find the Cube Root of that number.

2. What is a Cube of a Number according to RS Aggarwal Solutions Class 8 Chapter-4 Cubes and Cube Roots (Ex 4B) Exercise 4?

When a number is multiplied three times by itself, the resultant number (product) is known as the Cube of the given number. This is known as a Cube because it helps to represent the volume of Cube. In other words, a number raised to exponent 3 is called the Cube of that number. For example, the Cube of 4 is 64. That means 4 × 4 × 4 = 64, and it can be written as 43. To find the Cube of a number, first, multiply that number by itself, then multiply the product obtained with the original number again. For example, to find the Cube of 7, we will first find the value of 7 × 7. This value is 49. Now, we will find 49 × 7. This is equal to 343. Hence, we can say that the number 7 is 343.

3. How to find a Cube of a negative number according to RS Aggarwal Solutions Class 8 Chapter-4 Cubes and Cube Roots (Ex 4B) Exercise 4?

The process for finding the Cube of a negative number is the same as that of a whole number and fraction. Remember that the Cube of a negative number is always negative, while the Cube of a positive number is always positive. For example, let us try finding the Cube of -7.

We know that the Cube of -7 is (-7) × (-7) × (-7). Now, in order to find the Cube of (-7), we will first find the value of (-7) × (-7). This value is 49. Now, we will find 49 × (-7). This is equal to -343. Hence, it proves that the Cube of the number -7 is -343.

4. How will you find the Cube Root of 343?

The Cube Root of 343 can be found as it is the number which when multiplied three times by itself gives 343 as the product. If we multiply 7 three times, we will get 343 as the product as 7 × 7 × 7 = 73 = 343 (We can use the prime factorization method to find this). Thus, the Cube Root of 343 is 7. Vedantu’s expert teaches us how to find the Cube Root of this number.

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