Squares, cubes and their roots, powers of small numbers, negative numbers squared, and estimating a root.
What you will learn
- Recall squares to 15² and cubes to 5³
- Work out powers and roots, with negatives
- Estimate a square root
- Use powers in the order of operations
Powers are repeated multiplication
- 4² (four squared) = 4 × 4 = 16, not 4 × 2.
- 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. The small number, the index, says how many times to multiply.
- √49 = 7 because 7² = 49. ∛64 = 4 because 4³ = 64. A negative number has a cube root: ∛(−8) = −2.
Learn the squares up to 15² = 225 and the cubes 1, 8, 27, 64, 125, and 1000 = 10³.
To find the square number between 390 and 420, take the square root of each end: √390 is just under 20 (20² = 400) and √420 is just over 20, so the square number is 20² = 400. For cubes, test cube numbers near the range: 7³ = 343 sits between 330 and 360.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Powers are repeated multiplication
- Negatives and brackets
- Try it: Powers on the calculator
7 practice questions, marked as you go; about 20 minutes in all.
Key terms
Index
In this unit: Powers, roots and standard form
Squares, cubes and roots, the laws of indices (negative and fractional too), and very large and very small numbers in standard form.