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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 $A_{n+1} + B_{n+1}\sqrt 2$.