Questions: ∛(6y+13) = ∛17

∛(6y+13) = ∛17
Transcript text: \(\sqrt[3]{6 y+13}=\sqrt[3]{17}\)
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Solution

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Solution Steps

Step 1: Cube both sides

To eliminate the cube roots, cube both sides of the equation: \[ \sqrt[3]{6y + 13} = \sqrt[3]{17} \] Cubing both sides gives: \[ 6y + 13 = 17 \]

Step 2: Solve for \( y \)

Subtract 13 from both sides to isolate the term with \( y \): \[ 6y = 17 - 13 \] \[ 6y = 4 \] Now, divide both sides by 6 to solve for \( y \): \[ y = \frac{4}{6} = \frac{2}{3} \]

Final Answer

\[ \boxed{y = \frac{2}{3}} \]

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