### Be Reasonable

Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.

### Good Approximations

Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.

### Rational Roots

Given that a, b and c are natural numbers show that if sqrt a+sqrt b is rational then it is a natural number. Extend this to 3 variables.

# The Root Cause

##### Stage: 5 Challenge Level:

Prove that if $a$ is an integer and not a square number then $\sqrt{a}$ is irrational.

NOTES AND BACKGROUND
If you have seen a proof that the square root of 2 is irrational the interactivity Proof Sorter may help you to understand the proof better. You can look this proof up in textbooks written for students in their last year of school mathematics or first year of university mathematics.