Question

Simplify the radical. What is the number under the radical sign when it is simplified? Do not rationalize the denominator. ∛-27/81. Please help asap^^

Answer 1

`-\frac{1}{\sqrt[3]{3}}`

Explanation:

To do this we can ask ourselves "What number multiplied three times by itself is _____?" In this case we have -27 and 81. We see that -3*-3*-3=-27. We also see that 3*3*3*3=81. This means that
`\sqrt[3]{-27}=-3,` and
`\sqrt[3]{81} = 3\sqrt[3]{3}.`

The fraction we get is
`\frac{-3}{3\sqrt[3]{3} }`, and we can simplify to get
`-\frac{1}{\sqrt[3]{3}}`.