Basic Math Examples

$\sqrt[3]{2 y + 3} - 1 = 0$

Step 1

Add $1$ to both sides of the equation.

$\sqrt[3]{2 y + 3} = 1$

Step 2

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

${\sqrt[3]{2 y + 3}}^{3} = 1^{3}$

Step 3

Simplify each side of the equation.

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Step 3.1

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

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

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Step 3.2.1.1

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

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Step 3.2.1.1.1

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

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

Step 3.2.1.1.2

Cancel the common factor of $3$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

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

Step 3.2.1.1.2.2

Rewrite the expression.

${(2 y + 3)}^{1} = 1^{3}$

Step 3.2.1.2

Simplify.

$2 y + 3 = 1^{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

One to any power is one.

$2 y + 3 = 1$

Step 4

Solve for $y$ .

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Step 4.1

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

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Step 4.1.1

Subtract $3$ from both sides of the equation.

$2 y = 1 - 3$

Step 4.1.2

Subtract $3$ from $1$ .

$2 y = - 2$

Step 4.2

Divide each term in $2 y = - 2$ by $2$ and simplify.

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Step 4.2.1

Divide each term in $2 y = - 2$ by $2$ .

$\frac{2 y}{2} = \frac{- 2}{2}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $2$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 2}{2}$

Step 4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 2}{2}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $- 2$ by $2$ .

$y = - 1$