RBSE Class 8 Maths Notes Chapter 7 Cube and Cube Roots

These comprehensive RBSE Class 8 Maths Notes Chapter 7 Cube and Cube Roots will give a brief overview of all the concepts.

RBSE Class 8 Maths Chapter 7 Notes Cube and Cube Roots

→ Perfect Cube: A natural number n is called a perfect cube or cube number if there exist a natural number ‘a’ such that
n = a × a × a = a³
Ex. 8 = 2 × 2 × 2 = 2³

→ Cubes of Negative Integers: The cubes of a negative integer are always negative. Ex. (- 1)³ = (- 1) × (- 1) × (- 1) = - 1

→ Cube of a rational number \left(\frac{a}{b}\right) is the cube of the numerator (a) divided by the cube of the denominator.

→ If in the prime factorisation of any number each factor appears three times, then the number is a perfect cube.

→ The symbol \(\sqrt[3]{}\) denotes cube root. Ex. \(\sqrt[3]{8}\) = 2

→ If the digits at the unit’s place of a number is 0, 1, 4, 5, 6 or 9, then the digit at the unit’s place of its cube will also be the same digit.

→ If the digit at the unit’s place of a number is 2, then the digits at the unit place of its cube is 8 and vice versa.

→ Cubes of a number ending with 3 or 7 ends with 7 or 3 respectively.

→ Cubes of all odd natural numbers are odd.

→ Cubes of all even natural numbers are even.

→ Cubes of negative integers are negative.

→ Cubes of a number ends with a zero, ends with three zeroes.

→ If a and b are any two whole numbers, then \(\sqrt[3]{a b}=\sqrt[3]{a} \times \sqrt[3]{b}\)

→ If a and b are any two whole numbers (b ≠ 0), then \(\sqrt[3]{\frac{a}{b}}=\frac{\sqrt[3]{a}}{\sqrt[3]{b}}\)