Year 9: Simplification of square and cubic roots

What are square roots?

A square root of a number is a value that, when multiplied by itself, equals the original number. We use the symbol √ to represent square roots.

Example: √9 = 3 because 3 x 3 = 9

Simplifying square roots

We simplify square roots by finding perfect square factors of the number inside the square root. A perfect square is a number that can be written as the product of a whole number and itself (e.g., 1, 4, 9, 16, 25, etc.).

Example: √18 = √(9 x 2) = √9 x √2 = 3√2

What are cubic roots?

A cubic root of a number is a value that, when multiplied by itself three times, equals the original number.

We use the symbol ∻ to represent cubic roots.

Simplifying cubic roots

Similar to square roots, we simplify cubic roots by finding perfect cube factors.

Example: ∻27 = ∻(27 x 1) = ∻(3 x 3 x 3) = 3

Important notes

• Always simplify as much as possible.
• Ensure your answer is in the simplest form.