Your mission: expand the number line
- Read the introduction to the real ones.
- Explore rational, irrational and approximations.
- Advance to inequalities and quadratic equations.
- Use the probability chapter as a supplementary application.
Diagonal challenge
A square has side 1. By Pythagoras’ theorem, its diagonal measures √2. Is this measure rational? Between which integers does it lie?
Check out the investigation
√2 is irrational. Since 1² < 2 < 2², we have 1 < √2 < 2. The approximation 1,414 is not the exact value of the diagonal.
To move forward: explain why a recurring decimal is rational and why an approximation does not identify the exact value of an irrational one.