What is the value of 64 3 - 1 64 3 ?

The cube root of any real number is that number which when raised to the power of 3 gives the answer equal to the number whose cube root is to be determined. The cube root of a number can also be exponentially represented as the number to the power 1 3 . Cube root of a number which is a perfect cube can be determined by the prime factorization method. The name prime factorization method is because the method involves the process of resolution of the number whose cube root is to be found into its prime factors. Now 64 = 4 × 4 × 4 = 4 3 ⇒ 64 3 = 4 3 3 ⇒ 64 3 = 4 Now , 64 3 - 1 64 3 = 4 - 1 4 = 16 - 1 4 ∴ 64 3 - 1 64 3 = 15 4

What is the value of 27 3 + - 27 3 ?

To simplify: 27 3 + - 27 3 We know that, x a a = x ⇒ 27 3 + - 27 3 = 3 3 3 + - 3 3 3 = 3 + - 3 = 3 - 3 = 0 Therefore, 27 3 + - 27 3 = 0

E M B I B E

Mathematics Textbook of Competency Based Questions for Class VIII>Chapter 6 - Cubes and Cube Roots>Exercise>Q 1

EASY

8th CBSE

IMPORTANT

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Interlocking cubes come in different colours. Different shapes can be created by joining them.

Sasha is making a large cube using small interlocking cubes.

She starts with a yellow cube and then its one layer of red cubes around it to make the large cube.

What is the number of red cubes used $?$

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Important Questions on Cubes and Cube Roots

EASY

8th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class VIII>Chapter 6 - Cubes and Cube Roots>Exercise>Q 3

Akshat has

35

interlocking cubes of the same colour. He made two large cubes of different side lengths using up all the small cubes. How many small cubes will be found along each side of the two large cubes made by him?