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The student will be able to Objectives The student will be able to simplify a cube root. SOL: A.13 2009

Cube Roots The index of a cube root is always 3. The cube root of 64 is written as .

The cube root of a number is… What does cube root mean? The cube root of a number is… …the value when multiplied by itself three times gives the original number.

Cube Root Vocabulary radical sign index radicand

Perfect Cubes If a number is a perfect cube, then you can find its exact cube root. A perfect cube is a number that can be written as the cube (raised to third power) of another number.

What are Perfect Cubes? 13 = 1 x 1 x 1 = 1 23 = 2 x 2 x 2 = 8 33 = 3 x 3 x 3 = 27 43 = 4 x 4 x 4 = 64 53 = 5 x 5 x 5 = 125 and so on and on and on…..

Examples: because because

Examples:

Examples:

Simplify Cube Roots Not all numbers or expressions have an exact cube root as in the previous examples. If a number is NOT a perfect cube, then you might be able to SIMPLIFY it.

To simplify a cube root ... 1 Write the radicand as a product of two factors, where one of the factors is a perfect cube. 2 Extract the cube root of the factor that is a perfect cube. 3 The factors that are not perfect cubes will remain as the radicand.

Examples: perfect cube 1) 2) 3)

cannot be simplified! Not all cube roots can be simplified! Example: 30 is not a perfect cube. 30 does not have a perfect cube factor. cannot be simplified!