Evaluate cube root of 2x+5=5

$\sqrt[3]{2 x + 5} = 5$

Step 1

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

${\sqrt[3]{2 x + 5}}^{3} = 5^{3}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2 x + 5}$ as ${(2 x + 5)}^{\frac{1}{3}}$ .

${({(2 x + 5)}^{\frac{1}{3}})}^{3} = 5^{3}$

Simplify the left side.

Simplify ${({(2 x + 5)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(2 x + 5)}^{\frac{1}{3}})}^{3}$ .

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

${(2 x + 5)}^{\frac{1}{3} \cdot 3} = 5^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(2 x + 5)}^{\frac{1}{3} \cdot 3} = 5^{3}$

Rewrite the expression.

${(2 x + 5)}^{1} = 5^{3}$

Simplify.

$2 x + 5 = 5^{3}$

Simplify the right side.

Raise $5$ to the power of $3$ .

$2 x + 5 = 125$

Step 3

Solve for $x$ .

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

Subtract $5$ from both sides of the equation.

$2 x = 125 - 5$

Subtract $5$ from $125$ .

$2 x = 120$

Divide each term in $2 x = 120$ by $2$ and simplify.

Divide each term in $2 x = 120$ by $2$ .

$\frac{2 x}{2} = \frac{120}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{120}{2}$

Divide $x$ by $1$ .

$x = \frac{120}{2}$

Simplify the right side.

Divide $120$ by $2$ .

$x = 60$