Estimating Roots

Between the perfect squares

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

• Most square roots are irrational: endless, non-repeating decimals.
• Trap a root between perfect squares, then refine.
• $\sqrt{n^2 + d} \approx n + \frac{d}{2n}$ for small $d$.

Steps

1. Most roots never end
2. Place the root
3. Using a known root
4. Root of 50
5. Squaring the rectangle
6. A cube root
7. Which is bigger?