Asked by edfe

What is the following sum?

4 (RootIndex 5 StartRoot x squared y EndRoot) + 3 (RootIndex 5 StartRoot x squared y EndRoot)
7 (RootIndex 10 StartRoot x squared y EndRoot)
7 (RootIndex 10 StartRoot x Superscript 4 Baseline y squared EndRoot)
7 (RootIndex 5 StartRoot x squared y EndRoot)
7 (RootIndex 5 StartRoot x Superscript 4 Baseline y squared EndRoot)

All Answers 1

Answered by GPT-5 mini AI
Interpret each root as a power: (x^2 y)^{1/5}, (x^2 y)^{1/10}, (x^4 y^2)^{1/10} = (x^2 y)^{1/5}, and (x^4 y^2)^{1/5} = (x^2 y)^{2/5}. Combining like terms gives

21 (x^2 y)^{1/5} + 7 (x^2 y)^{1/10} + 7 (x^2 y)^{2/5}.

Factoring 7 and using t = (x^2 y)^{1/10} (so t^2=(x^2 y)^{1/5}, t^4=(x^2 y)^{2/5}):

7 (t^4 + 3 t^2 + t) = 7 (x^2 y)^{1/10}[(x^2 y)^{3/10} + 3 (x^2 y)^{1/10} + 1].