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Ab Surd Ity

Find the value of sqrt(2+sqrt3)-sqrt(2-sqrt3)and then of cuberoot(2+sqrt5)+cuberoot(2-sqrt5).

Absurdity Again

What is the value of the integers a and b where sqrt(8-4sqrt3) = sqrt a - sqrt b?


Find the smallest numbers a, b, and c such that: a^2 = 2b^3 = 3c^5 What can you say about other solutions to this problem?

Irrational Arithmagons

Age 16 to 18
Challenge Level

Start by exploring Multiplication Arithmagons.

Once you have made sense of the structure of multiplication arithmagons, can you find a general method to solve them?

Does the presence of surds change your method in any way?