Example 4
Completion requirements
| Example 4 |
Solve \(\sqrt[3]{{3r - 2}} = 4\).
Step 1: Identify any restrictions on the variable.
Because the index is \(3\) (odd), there are no restrictions on the variable, \(r \in \rm R\).
Step 2: Raise both sides of the equation to the power of the index in order to remove the radical.
\(\begin{align}
\sqrt[3]{{3r - 2}} &= 4 \\
\left( {\sqrt[3]{{3r - 2}}} \right)^3 &= 4^3 \\
3r - 2 &= 64 \\
\end{align}\)
Step 3: Solve for the variable.
\(\begin{align}
3r - 2 &= 64 \\
3r &= 66 \\
r &= 22 \\
\end{align}\)
Step 4: Verify the solution.
The solution is \(r = 22\).
Because the index is \(3\) (odd), there are no restrictions on the variable, \(r \in \rm R\).
Step 2: Raise both sides of the equation to the power of the index in order to remove the radical.
\(\begin{align}
\sqrt[3]{{3r - 2}} &= 4 \\
\left( {\sqrt[3]{{3r - 2}}} \right)^3 &= 4^3 \\
3r - 2 &= 64 \\
\end{align}\)
Step 3: Solve for the variable.
\(\begin{align}
3r - 2 &= 64 \\
3r &= 66 \\
r &= 22 \\
\end{align}\)
Step 4: Verify the solution.
| Left Side | Right Side |
|---|---|
| \(\begin{array}{r} \sqrt[3]{{3r - 2}} \\ \sqrt[3]{{3\left( {22} \right) - 2}} \\ \sqrt[3]{{66 - 2}} \\ \sqrt[3]{{64}} \\ 4 \\ \end{array}\) | \(4\) |
| LS = RS \(\hspace{30pt}\) | |
The solution is \(r = 22\).