List

Indices and Surds

Climbing Powers
problem
Favourite

Climbing powers

Age
16 to 18
Challenge level
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$2\wedge 3\wedge 4$ 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 $\sqrt{2}$?
Power Stack
problem

Power stack

Age
16 to 18
Challenge level
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When you stack powers, how do you evaluate them?
Quick Sum
problem

Quick sum

Age
16 to 18
Challenge level
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Is this surd sum exactly 3?
Irrational arithmagons
problem

Irrational arithmagons

Age
16 to 18
Challenge level
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Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?