Algebra Examples

$y = \sqrt[3]{x - 2}$

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

$y = \sqrt[3]{(- 2) - 2}$

Step 2

Simplify $\sqrt[3]{(- 2) - 2}$ .

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Step 2.1

Subtract $2$ from $- 2$ .

$y = \sqrt[3]{- 4}$

Step 2.2

Rewrite $- 4$ as ${(- 1)}^{3} \cdot 4$ .

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Step 2.2.1

Rewrite $- 4$ as $- 1 (4)$ .

$y = \sqrt[3]{- 1 (4)}$

Step 2.2.2

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

$y = \sqrt[3]{{(- 1)}^{3} \cdot 4}$

Step 2.3

Pull terms out from under the radical.

$y = - 1 \sqrt[3]{4}$

Step 2.4

Rewrite $- 1 \sqrt[3]{4}$ as $- \sqrt[3]{4}$ .

$y = - \sqrt[3]{4}$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

$y = \sqrt[3]{(- 1) - 2}$

Step 4

Simplify $\sqrt[3]{(- 1) - 2}$ .

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Step 4.1

Subtract $2$ from $- 1$ .

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

Step 4.2

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

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Step 4.2.1

Rewrite $- 3$ as $- 1 (3)$ .

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

Step 4.2.2

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

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

Step 4.3

Pull terms out from under the radical.

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

Step 4.4

Rewrite $- 1 \sqrt[3]{3}$ as $- \sqrt[3]{3}$ .

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

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$y = \sqrt[3]{(0) - 2}$

Step 6

Simplify $\sqrt[3]{(0) - 2}$ .

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Step 6.1

Subtract $2$ from $0$ .

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

Step 6.2

Rewrite $- 2$ as ${(- 1)}^{3} \cdot 2$ .

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Step 6.2.1

Rewrite $- 2$ as $- 1 (2)$ .

$y = \sqrt[3]{- 1 (2)}$

Step 6.2.2

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

$y = \sqrt[3]{{(- 1)}^{3} \cdot 2}$

Step 6.3

Pull terms out from under the radical.

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

Step 6.4

Rewrite $- 1 \sqrt[3]{2}$ as $- \sqrt[3]{2}$ .

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

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

$y = \sqrt[3]{(1) - 2}$

Step 8

Simplify $\sqrt[3]{(1) - 2}$ .

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Step 8.1

Subtract $2$ from $1$ .

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

Step 8.2

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

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

Step 8.3

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

$y = - 1$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$y = \sqrt[3]{(2) - 2}$

Step 10

Simplify $\sqrt[3]{(2) - 2}$ .

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Step 10.1

Subtract $2$ from $2$ .

$y = \sqrt[3]{0}$

Step 10.2

Rewrite $0$ as $0^{3}$ .

$y = \sqrt[3]{0^{3}}$

Step 10.3

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

$y = 0$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & - \sqrt[3]{4} \\ - 1 & - \sqrt[3]{3} \\ 0 & - \sqrt[3]{2} \\ 1 & - 1 \\ 2 & 0 \end{array}$

Step 12