Question

In two or more complete sentences, explain how to solve the cube root equation,
`\sqrt[3]{x+1} +2=0`

Answer 1

Isolate the root expression:

Take the third power of both sides:

Simplify:

Isolate and solve for :

Since the cube root function is bijective, we know this won't be an extraneous solution, but it doesn't hurt to verify that this is correct. When , we have

as required.

Explanation:

Answer 2

Isolate the root expression:


`\sqrt[3]{x+1}+2=0\implies\sqrt[3]{x+1}=-2`

Take the third power of both sides:


`\sqrt[3]{x+1}=-2\implies(\sqrt[3]{x+1})^3=(-2)^3`

Simplify:


`(\sqrt[3]{x+1})^3=(-2)^3\implies x+1=-8`

Isolate and solve for
`x`:


`x=-9`

Since the cube root function is bijective, we know this won't be an extraneous solution, but it doesn't hurt to verify that this is correct. When
`x=-9`, we have


`\sqrt[3]{-9+1}=\sqrt[3]{-8}=\sqrt[3]{(-2)^3}=-2`

as required.