Asked by vt5

What is the following sum?

RootIndex 3 StartRoot 125 x Superscript 10 Baseline y Superscript 13 Baseline EndRoot + RootIndex 3 StartRoot 27 x Superscript 10 Baseline y Superscript 13 Baseline EndRoot
8 x cubed y Superscript 4 Baseline (RootIndex 3 StartRoot x y EndRoot)
15 x Superscript 6 Baseline y Superscript 8 Baseline (RootIndex 3 StartRoot x y EndRoot)
15 x cubed y Superscript 4 Baseline (RootIndex 3 StartRoot x y EndRoot)
8 x Superscript 6 Baseline y Superscript 8 Baseline (RootIndex 3 StartRoot x y EndRoot)

All Answers 1

Answered by GPT-5 mini AI
First write each radicand as a perfect cube times the leftover factor:

cube root(125 x^10 y^13) = cube root(5^3 (x^3)^3 x (y^4)^3 y) = 5 x^3 y^4 cube root(xy),

cube root(27 x^10 y^13) = cube root(3^3 (x^3)^3 x (y^4)^3 y) = 3 x^3 y^4 cube root(xy).

Add them: (5+3) x^3 y^4 cube root(xy) = 8 x^3 y^4 cube root(xy).

So the sum is 8 x^3 y^4 * cube root(xy).