19 Sep

### Radical Simplification - Not That Simple!

While the cube root of 2+sqrt(5) is in the extension field Q[sqrt(5)], the square root of 2+sqrt(3) is not in Q[sqrt(3)] but rather in Q[sqrt(2), sqrt(3)]

19 Sep

15 Sep

This amounts to a cubic equation for x=a+b: x^3+3x-36=0. The sum of the roots of this equation is -3, their product is 36, and the sum of their squares is 0. The latter implies that two of these are complex conjugates, say, u ± iv and one is a real number w (that is supposed to be 3.)

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