Solve for t 250=62.5 cube root of t+75.8

$250 = 62.5 \sqrt[3]{t} + 75.8$

Rewrite the equation as $62.5 \sqrt[3]{t} + 75.8 = 250$ .

$62.5 \sqrt[3]{t} + 75.8 = 250$

Move all terms not containing $62.5 \sqrt[3]{t}$ to the right side of the equation.

Subtract $75.8$ from both sides of the equation.

$62.5 \sqrt[3]{t} = 250 - 75.8$

Subtract $75.8$ from $250$ .

$62.5 \sqrt[3]{t} = 174.2$

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

${(62.5 \sqrt[3]{t})}^{3} = {174.2}^{3}$

Simplify each side of the equation.

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

${(62.5 t^{\frac{1}{3}})}^{3} = {174.2}^{3}$

Simplify the left side.

Simplify ${(62.5 t^{\frac{1}{3}})}^{3}$ .

Apply the product rule to $62.5 t^{\frac{1}{3}}$ .

${62.5}^{3} {(t^{\frac{1}{3}})}^{3} = {174.2}^{3}$

Raise $62.5$ to the power of $3$ .

$244140.625 {(t^{\frac{1}{3}})}^{3} = {174.2}^{3}$

Multiply the exponents in ${(t^{\frac{1}{3}})}^{3}$ .

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

$244140.625 t^{\frac{1}{3} \cdot 3} = {174.2}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$244140.625 t^{\frac{1}{3} \cdot 3} = {174.2}^{3}$

Rewrite the expression.

$244140.625 t^{1} = {174.2}^{3}$

Simplify.

$244140.625 t = {174.2}^{3}$

Simplify the right side.

Raise $174.2$ to the power of $3$ .

$244140.625 t = 5286210.488$

Divide each term in $244140.625 t = 5286210.488$ by $244140.625$ and simplify.

Divide each term in $244140.625 t = 5286210.488$ by $244140.625$ .

$\frac{244140.625 t}{244140.625} = \frac{5286210.488}{244140.625}$

Simplify the left side.

Cancel the common factor of $244140.625$ .

Cancel the common factor.

$\frac{244140.625 t}{244140.625} = \frac{5286210.488}{244140.625}$

Divide $t$ by $1$ .

$t = \frac{5286210.488}{244140.625}$

Simplify the right side.

Divide $5286210.488$ by $244140.625$ .

$t = 21.65231815$