Comparing sqrt(3)+cbrt(2) and 3 | Suggested by Juan Pablo

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Nice question, because they are very close to each other. My calculator days that the sum of radikale is about 2.99197 and thus smaller.
Considering how to do an algebraic proof...

goldfing
Автор

"And you get the following:" and then just writing the result of cubing, without any intermediate calculation, is not serious IMHO. It pretends less effort than it reallly is. We must a least calculate
(3 - sqrt(3))^3
= 27 - sqrt(27) - 9*sqrt(3)*(3 - sqrt(3))
= 27 - 3*sqrt(3) - 27*sqrt(3) + 27
= 54 - 30*sqrt(3).

goldfing
Автор

4:50 why would you assume these don't sum to exactly 3? when you did the math and found the equation didn't balance (2700 vs 2704) didn't you demonstrate the sides weren't equal?

tonyennis
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