Big Idea
Powers are repeated multiplication; roots undo powers.
Powers and Roots
Use squares, cubes, square roots, cube roots, and simple index notation.
Understand it first
Square
5 squared means 5 x 5.
Cube
3 cubed means 3 x 3 x 3.
Root
The square root of 49 is the number that squares to make 49.
Method Ladder
Use this same ladder every time you meet this topic.
- Read the power or root symbol carefully.
- Write it as multiplication if needed.
- Calculate step by step.
- Use inverse checks for roots.
Worked example: Calculate 4 cubed
- 4 cubed means 4 x 4 x 4.
- 4 x 4 = 16.
- 16 x 4 = 64.
- Answer: 64.
Fix It Lab
Read these before the quiz. They are the traps that lose marks.
- Common mistakeThinking 5 squared means 5 x 2.
- Common mistakeForgetting that roots undo powers.
- Common mistakeRushing powers without expanding them.
Top-mark challenge
Open challenge
Explain why the square root of 81 is 9.
Write full working and one sentence explaining the method.
10-question unlock quiz
The quiz is now on separate pages. You answer one question, then the next question opens. Finish Question 10 to complete this mission.
Start Question 1