M4.1.3 For the adult
Roots and fractional powers
What can it mean to raise 9 to the power 1/2?
What this chapter teaches
A power of 1/2 is a square root, and a power of 1/3 is a cube root, because the root multiplies back to the number. A power such as 2/3 means root first, then power. Odd roots of negative numbers exist. Even roots of them do not, in the real numbers.
Three questions to ask
There is no one right wording. Listen for the idea.
- Why must 9 to the power 1/2 be 3 and not 4.5?
- What is the cube root of −27, and how can you check it?
- How do you work out 8 to the power 2/3 in two steps?
After the chapter, the learner can
- Find the cube root of 64 and of −8
- Read 9 to the power 1/2 as √9
- Work out 8 to the power 2/3
What they copy into their notebook
A power of 1/2 is a square root. A power of 1/3 is a cube root. With 2/3: root first, then power. The cube root of −8 is −2. No real square root of −9.