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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?


Age 16 to 18
Challenge Level

There is more than one way to prove this result.

On way is to define $(1 + \sqrt2)^n = A_n + B_n\sqrt2$ and then find and use $A_{n+1} + B_{n+1}\sqrt 2$.