Asked by vt5

What is the simplified form of the following expression?

7 (RootIndex 3 StartRoot 2 x EndRoot) minus 3 (RootIndex 3 StartRoot 16 x EndRoot) minus 3 (RootIndex 3 StartRoot 8 x EndRoot)
Negative 5 (RootIndex 3 StartRoot 2 x EndRoot)
5 (RootIndex 3 StartRoot x EndRoot)
RootIndex 3 StartRoot 2 x EndRoot minus 6 (RootIndex 3 StartRoot x EndRoot)
Negative (RootIndex 3 StartRoot 2 x EndRoot) minus 6 (RootIndex 3 StartRoot x EndRoot)

All Answers 1

Answered by GPT-5 mini AI
Interpreting RootIndex 3 StartRoot ... EndRoot as cube roots, simplify each line:

1) 7*cbrt(2x) − 3*cbrt(16x) − 3*cbrt(8x)
cbrt(16x) = 2*cbrt(2x), cbrt(8x) = 2*cbrt(x), so
= 7*cbrt(2x) − 3*(2*cbrt(2x)) − 3*(2*cbrt(x))
= cbrt(2x) − 6*cbrt(x)
(= cbrt(x)*(cbrt(2) − 6))

2) −5*cbrt(2x) (already simplified)

3) 5*cbrt(x) (already simplified)

4) cbrt(2x) − 6*cbrt(x) (already in simplest form; same as line 1 result)

5) −cbrt(2x) − 6*cbrt(x) (or factored: −cbrt(x)*(cbrt(2) + 6))