Prompt: Marc solves the equation Latex: (\sqrt[4]{x})^3=5\textsf{.} His work is shown below.

Step 1: Latex: (\sqrt[4]{x})^3=5
(
√
[
4
]
x
)
3
=
5

Step 2: Latex: x^{\frac{3}{4} }=5
x
3
4
=
5

Step 3: Latex: x^{\frac{3}{4} \cdot \frac{4}{3} }=5^{\frac{4}{3} }
x
3
4
⋅
4
3
=
5
4
3

Step 4: Latex: x=\sqrt[3]{5 \cdot 5 \cdot 5 \cdot 5}
x
=
√
[
3
]
5
⋅
5
⋅
5
⋅
5

Step 5: Latex: x=5\sqrt[3]{\not{5} \cdot \not{5} \cdot\not {5} \cdot 5}
x
=
5
√
[
3
]
¬
5
⋅
¬
5
⋅
¬
5
⋅
5

Step 6: Latex: x=5\sqrt[3]{5}
x
=
5
√
[
3
]
5

Explain what Marc did in steps 4 and 5.

Why did he do this?

Create your own radical equation and explain how to solve it.

Is there an extraneous solution to your equation?