Year 8: Simplification of square and cubic roots

This cheat sheet will help you simplify square and cubic roots. Remember, a square root finds the number that, when multiplied by itself, equals the original number. A cubic root finds the number that, when multiplied by itself three times, equals the original number.

Simplifying Square Roots

• Finding the Square Root: The square root of a number is written as √x.
• Perfect Squares: A perfect square is a number that can be written as the square of an integer. Examples: 9 (√9 = 3), 16 (√16 = 4), 25 (√25 = 5).
• Simplifying Expressions: To simplify, find the largest perfect square that divides evenly into the number under the square root. Example: √18 = √(9 * 2) = √9 * √2 = 3√2.

Simplifying Cubic Roots

• Finding the Cubic Root: The cubic root of a number is written as ∛x.
• Perfect Cubes: A perfect cube is a number that is the cube of an integer. Examples: 8 (∛8 = 2), 27 (∛27 = 3), 64 (∛64 = 4).
• Simplifying Expressions: To simplify, find the largest perfect cube that divides evenly into the number under the cubic root. Example: ∛72 = ∛8 * ∛9 = 2∛9

Practice is key: Try to simplify more square and cubic roots.