Squares, square roots, cubes and cube roots — KCSE Mathematics

To find the cube of a number, multiply the number by itself three times. For example, the cube of 3 is calculated as follows:

3³ = 3 × 3 × 3 = 27.

To find the cube root of a number, determine which number, when cubed, gives the original number. The cube root of 27 is:

∛27 = 3, because 3³ = 27.

You can also use factorization to find cubes and cube roots. For example, to find the cube of 4:

4³ = 4 × 4 × 4 = 64.

For factorization, consider the number 64. The prime factorization of 64 is:

64 = 2 × 2 × 2 × 2 × 2 × 2 = 2⁶.

To find the cube root of 64 using prime factors, divide the exponent by 3:

∛64 = ∛(2⁶) = 2^(6/3) = 2² = 4.

In mathematics, evaluating expressions involving squares, square roots, cubes, and cube roots is essential. Squares are calculated by multiplying a number by itself, while cubes involve multiplying a number by itself twice. Square roots and cube roots are the inverse operations of squaring and cubing, respectively.

To evaluate these expressions, follow these steps:

• For squares, use the formula: ( a^2 = a \times a )
• For cubes, use: ( a^3 = a \times a \times a )
• For square roots, find a number ( b ) such that ( b^2 = a )
• For cube roots, find a number ( c ) such that ( c^3 = a )

Example 1: Evaluate ( 5^2 ).

• ( 5^2 = 5 \times 5 = 25 )

Example 2: Evaluate ( \sqrt{64} ).

• The number that squares to 64 is 8, hence ( \sqrt{64} = 8 ).

Practicing these operations will enhance your problem-solving skills and boost your confidence in mathematics!