Solve by Factoring cube root of x+4=6

$\sqrt[3]{x + 4} = 6$

Step 1

Subtract $6$ from both sides of the equation.

$\sqrt[3]{x + 4} - 6 = 0$

Step 2

Add $6$ to both sides of the equation.

$\sqrt[3]{x + 4} = 6$

Step 3

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

${\sqrt[3]{x + 4}}^{3} = 6^{3}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x + 4}$ as ${(x + 4)}^{\frac{1}{3}}$ .

${({(x + 4)}^{\frac{1}{3}})}^{3} = 6^{3}$

Simplify the left side.

Simplify ${({(x + 4)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(x + 4)}^{\frac{1}{3}})}^{3}$ .

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

${(x + 4)}^{\frac{1}{3} \cdot 3} = 6^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(x + 4)}^{\frac{1}{3} \cdot 3} = 6^{3}$

Rewrite the expression.

${(x + 4)}^{1} = 6^{3}$

Simplify.

$x + 4 = 6^{3}$

Simplify the right side.

Raise $6$ to the power of $3$ .

$x + 4 = 216$

Step 5

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

Subtract $4$ from both sides of the equation.

$x = 216 - 4$

Subtract $4$ from $216$ .

$x = 212$