You may also like

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.

Continued Fractions II

In this article we show that every whole number can be written as a continued fraction of the form k/(1+k/(1+k/...)).

Rational Roots

Age 16 to 18 Challenge Level:

Suppose that a and b are natural numbers. If $\sqrt{a} + \sqrt{b}$ is rational then show that it is a natural number. Show that, indeed both $\sqrt{a}$ and $\sqrt{b}$ are then integers.

Suppose that a, b and c are natural numbers. If $\sqrt{a} + \sqrt{b} + \sqrt{c}$ is rational then show that it is a natural number. Moreover show that $\sqrt{a}$ , $\sqrt{b}$ and $\sqrt{c}$ are then integers.