Class 8 Maths: Cubes and Cube Roots Olympiad Questions

Cube

When you raise a number to power 3, it is called a cube. x3 = x * x * x when x is a number.

• If n = m3 and m is a natural number, then n is a perfect cube.
• Even natural numbers have the same cube.
• Natural numbers with odd cubes are odd.
• Negative numbers always have negative cubes.
• For first n natural numbers, their sum equals the sum of their cubes.
• Numbers ending in the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are represented by the digits 0, 1, 8, 1, 7, 5, 6, 3, 2, 9. All cubes of numbers ending in 0 and 1, 4, 5, 6, and 9 contain the same digit.
• Numbers ending with digits 2 ends in 8, and numbers are ending with digits 8 ends in 2.
• The cube of a number ending in 3 is 7, and the cube of a number ending in 7 is 3.

Cubes root

Numbers whose cube is x are said to have cube roots. X 3 denotes a cube root.

A perfect cube can be resolved into its cube root by dividing it into prime factors, then triple the prime factors, and choosing one out of each triplet to be its cube root.

Cubes Relation with Cube Numbers

Cubes are solid figures whose edges are perpendicular to each other and equal in length.

As an example, consider a cube with unit sides. The 27 units contained in a 3 unit cube are calculated by arranging these cubes to form a bigger cube.

A cube of four units will contain 64 cubes of the same type.

A Cube Number with Units Digits

If an even or odd number is multiplied by its cube, the resulting cube number will be equally odd or even.

• Cube numbers are divisible by the unit digit.
• Odd numbers have odd unit digits, and so do odd cube numbers.
• Numbers whose unit digits are even are also even in cube numbers.