Solve for r cube root of r+19=3

$\sqrt[3]{r + 19} = 3$

Step 1

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

${\sqrt[3]{r + 19}}^{3} = 3^{3}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{r + 19}$ as ${(r + 19)}^{\frac{1}{3}}$ .

${({(r + 19)}^{\frac{1}{3}})}^{3} = 3^{3}$

Simplify the left side.

Simplify ${({(r + 19)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(r + 19)}^{\frac{1}{3}})}^{3}$ .

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

${(r + 19)}^{\frac{1}{3} \cdot 3} = 3^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(r + 19)}^{\frac{1}{3} \cdot 3} = 3^{3}$

Rewrite the expression.

${(r + 19)}^{1} = 3^{3}$

Simplify.

$r + 19 = 3^{3}$

Simplify the right side.

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

$r + 19 = 27$

Step 3

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

Subtract $19$ from both sides of the equation.

$r = 27 - 19$

Subtract $19$ from $27$ .

$r = 8$