Basic Math Examples

$\sqrt[3]{3 n + 5} = \sqrt[3]{6 n - 4}$

Step 1

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

${\sqrt[3]{3 n + 5}}^{3} = {\sqrt[3]{6 n - 4}}^{3}$

Step 2

Simplify each side of the equation.

Tap for more steps...

Step 2.1

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

${({(3 n + 5)}^{\frac{1}{3}})}^{3} = {\sqrt[3]{6 n - 4}}^{3}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

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

Tap for more steps...

Step 2.2.1.1

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

Tap for more steps...

Step 2.2.1.1.1

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

${(3 n + 5)}^{\frac{1}{3} \cdot 3} = {\sqrt[3]{6 n - 4}}^{3}$

Step 2.2.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.1.1.2.1

Cancel the common factor.

${(3 n + 5)}^{\frac{1}{3} \cdot 3} = {\sqrt[3]{6 n - 4}}^{3}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(3 n + 5)}^{1} = {\sqrt[3]{6 n - 4}}^{3}$

Step 2.2.1.2

Simplify.

$3 n + 5 = {\sqrt[3]{6 n - 4}}^{3}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Simplify ${\sqrt[3]{6 n - 4}}^{3}$ .

Tap for more steps...

Step 2.3.1.1

Factor $2$ out of $6 n - 4$ .

Tap for more steps...

Step 2.3.1.1.1

Factor $2$ out of $6 n$ .

$3 n + 5 = {\sqrt[3]{2 (3 n) - 4}}^{3}$

Step 2.3.1.1.2

Factor $2$ out of $- 4$ .

$3 n + 5 = {\sqrt[3]{2 (3 n) + 2 (- 2)}}^{3}$

Step 2.3.1.1.3

Factor $2$ out of $2 (3 n) + 2 (- 2)$ .

$3 n + 5 = {\sqrt[3]{2 (3 n - 2)}}^{3}$

Step 2.3.1.2

Rewrite ${\sqrt[3]{2 (3 n - 2)}}^{3}$ as $2 (3 n - 2)$ .

Tap for more steps...

Step 2.3.1.2.1

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

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

Step 2.3.1.2.2

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

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

Step 2.3.1.2.3

Combine $\frac{1}{3}$ and $3$ .

$3 n + 5 = {(2 (3 n - 2))}^{\frac{3}{3}}$

Step 2.3.1.2.4

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.3.1.2.4.1

Cancel the common factor.

$3 n + 5 = {(2 (3 n - 2))}^{\frac{3}{3}}$

Step 2.3.1.2.4.2

Rewrite the expression.

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

Step 2.3.1.2.5

Simplify.

$3 n + 5 = 2 (3 n - 2)$

Step 2.3.1.3

Apply the distributive property.

$3 n + 5 = 2 (3 n) + 2 \cdot - 2$

Step 2.3.1.4

Multiply.

Tap for more steps...

Step 2.3.1.4.1

Multiply $3$ by $2$ .

$3 n + 5 = 6 n + 2 \cdot - 2$

Step 2.3.1.4.2

Multiply $2$ by $- 2$ .

$3 n + 5 = 6 n - 4$

Step 3

Solve for $n$ .

Tap for more steps...

Step 3.1

Move all terms containing $n$ to the left side of the equation.

Tap for more steps...

Step 3.1.1

Subtract $6 n$ from both sides of the equation.

$3 n + 5 - 6 n = - 4$

Step 3.1.2

Subtract $6 n$ from $3 n$ .

$- 3 n + 5 = - 4$

Step 3.2

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

Tap for more steps...

Step 3.2.1

Subtract $5$ from both sides of the equation.

$- 3 n = - 4 - 5$

Step 3.2.2

Subtract $5$ from $- 4$ .

$- 3 n = - 9$

Step 3.3

Divide each term in $- 3 n = - 9$ by $- 3$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $- 3 n = - 9$ by $- 3$ .

$\frac{- 3 n}{- 3} = \frac{- 9}{- 3}$

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Cancel the common factor of $- 3$ .

Tap for more steps...

Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 3 n}{- 3} = \frac{- 9}{- 3}$

Step 3.3.2.1.2

Divide $n$ by $1$ .

$n = \frac{- 9}{- 3}$

Step 3.3.3

Simplify the right side.

Tap for more steps...

Step 3.3.3.1

Divide $- 9$ by $- 3$ .

$n = 3$