Unit 8, Lesson 15
Cube Roots
Grade 8
15.3
Activity
The numbers , , and are positive, and:
- Plot , , and on the number line. Be prepared to share your reasoning with the class.
- Plot on the number line.
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Decide mentally whether each statement is true.
The value of a cube root of a number lies between two integers. Which are those consecutive whole numbers for the following? Be prepared to explain your reasoning.
The numbers , , and are positive, and:
Like square roots, most cube roots of whole numbers are irrational. The only time the cube root of a number is a rational number is when the number we are taking the cube root of is a perfect cube. For example, 8 is a perfect cube, and .
We can approximate the values of the cube root of a number by observing the integers around it and remembering the relationship between cubes and cube roots. For example, is between 2 and 3 since and , and 20 is between 8 and 27. Similarly, since 100 is between and , we know is between 4 and 5.
Many calculators have a cube root function which can be used to approximate the value of a cube root more precisely. Using our numbers from before, a calculator will show that and that .