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RD Sharma Solutions for Class 8 Maths Chapter 4: Cubes and Cube Roots

The chapter covers all the concepts of cubes and cube roots. In Maths Chapter 4, Cubes and Cube Roots, cube number and cube root concepts, cube root through prime factorisation method, finding the cube roots of the cubic numbers through the estimation method, patterns of cube numbers.

When a number is multiplied thrice with its value, it is termed as a cube. For example, 27 is the cube of three as when 3 is multiplied by itself thrice, i.e.,3 x 3 x 3, the answer is 27. There are some tricks to determine the cubes or cube roots by observing the given number's last digit. The chapter has many explanations for many digits like 3, 7, 11. These tricks are helpful to simplify your problem-solving. The cube root is just the inverse procedure of deriving the cube. The cube root of 27 is 3. The symbol '∛' represents the cube root. As a result, ∛27 = 3

If each prime factor appears three times in the prime factorisation of any number, the number is the perfect cube. Typically, we must determine the smallest natural number by which a number may be multiplied or divided to form a perfect cube. Utilising the division technique to get the root of a cube is comparable to using the long division method or the manual square method. First, make a set of three-digit numbers from the rear to the centre. The next step is to discover a number whose cube root is smaller than or equal to that number's cube root. Cube root through the prime factorisation method is taught to the students in this chapter. First, the number is divided into its prime factors using the prime factorisation method. This step is necessary because breaking down numbers is required to find whether its factors are present in a set of threes or not. Now arrange the numbers obtained and arrange them in a set of three. For example, 216= 2*2*2*3*3*3, here 2 and 3 are arranged in sets of three. It can also be written as 216 = 6*6*6; thus, 216 can be said as the cube of 6 or 6 can be said as the cube root of 216.

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  • The solutions provide a comprehensive understanding of every segment essential for acing this chapter, and they help students master the topic thoroughly.

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