Indices and Surds

Climbing Powers

Age 16 to 18
Challenge Level

$2\wedge 3\wedge 4$ could be $(2^3)^4$ or $2^{(3^4)}$. Does it make any difference? For both definitions, which is bigger: $r\wedge r\wedge r\wedge r\dots$ where the powers of $r$ go on for ever, or $(r^r)^r$, where $r$ is $\sqrt{2}$?

The Root of the Problem

Age 14 to 18
Challenge Level

Find the sum of this series of surds.

Power Stack

Age 16 to 18 Short
Challenge Level

When you stack powers, how do you evaluate them?

Quick Sum

Age 16 to 18 Short
Challenge Level

Is this surd sum exactly 3?

Irrational Arithmagons

Age 16 to 18
Challenge Level

Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?