Asked by vt5
What is the following sum?
5 (RootIndex 3 StartRoot x EndRoot) + 9 (RootIndex 3 StartRoot x EndRoot)
14 (RootIndex 6 StartRoot x EndRoot)
14 (RootIndex 6 StartRoot x squared EndRoot)
14 RootIndex 3 StartRoot x EndRoot)
14 (RootIndex 3 StartRoot x squared EndRoot)
All Answers 1
Answered by
GPT-5 mini
AI
Interpreting RootIndex 3 as cube root and RootIndex 6 as sixth root, the terms are
5∛x + 9∛x + 14·⁶√x + 14·⁶√(x²) + 14∛x + 14∛(x²).
Note ⁶√(x²) = x^(2/6) = x^(1/3) = ∛x. So combine like terms:
∛x terms: 5+9+14+14 = 42, so 42∛x.
⁶√x term: 14·⁶√x = 14 x^(1/6).
∛(x²) term: 14∛(x²) = 14 x^(2/3).
Total:
14 x^(1/6) + 42 x^(1/3) + 14 x^(2/3)
You can factor 14 x^(1/6) if you like:
14 x^(1/6) (1 + 3 x^(1/6) + x^(1/2)).
5∛x + 9∛x + 14·⁶√x + 14·⁶√(x²) + 14∛x + 14∛(x²).
Note ⁶√(x²) = x^(2/6) = x^(1/3) = ∛x. So combine like terms:
∛x terms: 5+9+14+14 = 42, so 42∛x.
⁶√x term: 14·⁶√x = 14 x^(1/6).
∛(x²) term: 14∛(x²) = 14 x^(2/3).
Total:
14 x^(1/6) + 42 x^(1/3) + 14 x^(2/3)
You can factor 14 x^(1/6) if you like:
14 x^(1/6) (1 + 3 x^(1/6) + x^(1/2)).
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