Roots

Undoing powers

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• $\sqrt{a} = a^{1/2}$ and $\sqrt[n]{a} = a^{1/n}$; cube roots undo cubing.
• $\sqrt{ab} = \sqrt a \sqrt b$: pull out square factors to simplify.
• Roots don’t split over addition.

Steps

1. Side of a square
2. Roots as fractional powers
3. A cube
4. Fractional power
5. Simplify a root
6. A square of area 50
7. A common slip