Algebra Examples

$\sqrt[3]{x - 1}$

Step 1

Write $\sqrt[3]{x - 1}$ as an equation.

$y = \sqrt[3]{x - 1}$

Step 2

Find the x-intercepts.

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Step 2.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \sqrt[3]{x - 1}$

Step 2.2

Solve the equation.

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Step 2.2.1

Rewrite the equation as $\sqrt[3]{x - 1} = 0$ .

$\sqrt[3]{x - 1} = 0$

Step 2.2.2

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

${\sqrt[3]{x - 1}}^{3} = 0^{3}$

Step 2.2.3

Simplify each side of the equation.

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Step 2.2.3.1

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

${({(x - 1)}^{\frac{1}{3}})}^{3} = 0^{3}$

Step 2.2.3.2

Simplify the left side.

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Step 2.2.3.2.1

Simplify ${({(x - 1)}^{\frac{1}{3}})}^{3}$ .

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Step 2.2.3.2.1.1

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

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Step 2.2.3.2.1.1.1

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

${(x - 1)}^{\frac{1}{3} \cdot 3} = 0^{3}$

Step 2.2.3.2.1.1.2

Cancel the common factor of $3$ .

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Step 2.2.3.2.1.1.2.1

Cancel the common factor.

${(x - 1)}^{\frac{1}{3} \cdot 3} = 0^{3}$

Step 2.2.3.2.1.1.2.2

Rewrite the expression.

${(x - 1)}^{1} = 0^{3}$

Step 2.2.3.2.1.2

Simplify.

$x - 1 = 0^{3}$

Step 2.2.3.3

Simplify the right side.

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Step 2.2.3.3.1

Raising $0$ to any positive power yields $0$ .

$x - 1 = 0$

Step 2.2.4

Add $1$ to both sides of the equation.

$x = 1$

Step 2.3

x-intercept(s) in point form.

x-intercept(s): $(1, 0)$

Step 3

Find the y-intercepts.

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Step 3.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \sqrt[3]{(0) - 1}$

Step 3.2

Simplify $\sqrt[3]{(0) - 1}$ .

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Step 3.2.1

Subtract $1$ from $0$ .

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

Step 3.2.2

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$y = \sqrt[3]{{(- 1)}^{3}}$

Step 3.2.3

Pull terms out from under the radical, assuming real numbers.

$y = - 1$

Step 3.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 1)$

Step 4

List the intersections.

x-intercept(s): $(1, 0)$

y-intercept(s): $(0, - 1)$

Step 5