Solve the Rational Equation for x cube root of x-2=3

$\sqrt[3]{x - 2} = 3$

Step 1

To remove the radical on the left side of the equation, cube both sides of the equation.

${\sqrt[3]{x - 2}}^{3} = 3^{3}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x - 2}$ as ${(x - 2)}^{\frac{1}{3}}$ .

${({(x - 2)}^{\frac{1}{3}})}^{3} = 3^{3}$

Simplify the left side.

Simplify ${({(x - 2)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(x - 2)}^{\frac{1}{3}})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(x - 2)}^{\frac{1}{3} \cdot 3} = 3^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(x - 2)}^{\frac{1}{3} \cdot 3} = 3^{3}$

Rewrite the expression.

${(x - 2)}^{1} = 3^{3}$

Simplify.

$x - 2 = 3^{3}$

Simplify the right side.

Raise $3$ to the power of $3$ .

$x - 2 = 27$

Step 3

Move all terms not containing $x$ to the right side of the equation.

Add $2$ to both sides of the equation.

$x = 27 + 2$

Add $27$ and $2$ .

$x = 29$