Mathematics Class VIII: Cube Root Calculation

Cube Roots and Prime Factorization

• The cube root of 10648 is 22, as calculated using prime factorization.
• 10648 can be expressed as 2 x 2 x 2 x 11 x 11 x 11, which is the same as (2 x 11)³.

Perfect Cubes

• A perfect cube does not end with two zeros. This is because the cube of any number ending in 0 will also end in 000.

• If the square of a number ends in 5, then its cube also ends with 25.

• For example, 5² = 25 and 5³ = 125.

Cube Root Estimation

• The cube root of 1,331 is 11. This can be guessed by knowing that 10³= 1000 and 12³= 1728, and 1331 falls between these two numbers.

Sum of Cubes

• 32832 can be expressed as the sum of two cubes in two different ways:
  • 32832 = 32³ + 16³
  • 32832 = 30³ + 28³

Cube of Two-Digit Numbers

• The statement 'The cube of a two-digit number may have seven or more digits' is false.
• The cube of a two-digit number will always have five or six digits. For example, the cube of 99 is 970299, which has six digits.

Cube Root of 46656

• The cube root of 46656 is 36, obtained by prime factorization.
• 46656 can be expressed as 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3, which is (2 x 3 x 3)³ = 36³.