Finite Math Examples

$\sqrt[3]{x} (\sqrt[3]{56 x^{2}} - \sqrt[3]{x})$

Step 1

Simplify each term.

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Step 1.1

Rewrite $56 x^{2}$ as $2^{3} \cdot (7 x^{2})$ .

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Step 1.1.1

Factor $8$ out of $56$ .

$\sqrt[3]{x} (\sqrt[3]{8 (7) x^{2}} - \sqrt[3]{x})$

Step 1.1.2

Rewrite $8$ as $2^{3}$ .

$\sqrt[3]{x} (\sqrt[3]{2^{3} \cdot 7 x^{2}} - \sqrt[3]{x})$

Step 1.1.3

Add parentheses.

$\sqrt[3]{x} (\sqrt[3]{2^{3} \cdot (7 x^{2})} - \sqrt[3]{x})$

Step 1.2

Pull terms out from under the radical.

$\sqrt[3]{x} (2 \sqrt[3]{7 x^{2}} - \sqrt[3]{x})$

Step 2

Simplify by multiplying through.

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Step 2.1

Apply the distributive property.

$\sqrt[3]{x} (2 \sqrt[3]{7 x^{2}}) + \sqrt[3]{x} (- \sqrt[3]{x})$

Step 2.2

Reorder.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$2 \sqrt[3]{x} \sqrt[3]{7 x^{2}} + \sqrt[3]{x} (- \sqrt[3]{x})$

Step 2.2.2

Rewrite using the commutative property of multiplication.

$2 \sqrt[3]{x} \sqrt[3]{7 x^{2}} - \sqrt[3]{x} \sqrt[3]{x}$

Step 3

Simplify each term.

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Step 3.1

Multiply $2 \sqrt[3]{x} \sqrt[3]{7 x^{2}}$ .

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Step 3.1.1

Combine using the product rule for radicals.

$2 \sqrt[3]{7 x^{2} x} - \sqrt[3]{x} \sqrt[3]{x}$

Step 3.1.2

Raise $x$ to the power of $1$ .

$2 \sqrt[3]{7 (x^{1} x^{2})} - \sqrt[3]{x} \sqrt[3]{x}$

Step 3.1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 \sqrt[3]{7 x^{1 + 2}} - \sqrt[3]{x} \sqrt[3]{x}$

Step 3.1.4

Add $1$ and $2$ .

$2 \sqrt[3]{7 x^{3}} - \sqrt[3]{x} \sqrt[3]{x}$

Step 3.2

Reorder $7$ and $x^{3}$ .

$2 \sqrt[3]{x^{3} \cdot 7} - \sqrt[3]{x} \sqrt[3]{x}$

Step 3.3

Pull terms out from under the radical.

$2 (x \sqrt[3]{7}) - \sqrt[3]{x} \sqrt[3]{x}$

Step 3.4

Multiply $- \sqrt[3]{x} \sqrt[3]{x}$ .

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Step 3.4.1

Raise $\sqrt[3]{x}$ to the power of $1$ .

$2 x \sqrt[3]{7} - ({\sqrt[3]{x}}^{1} \sqrt[3]{x})$

Step 3.4.2

Raise $\sqrt[3]{x}$ to the power of $1$ .

$2 x \sqrt[3]{7} - ({\sqrt[3]{x}}^{1} {\sqrt[3]{x}}^{1})$

Step 3.4.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 x \sqrt[3]{7} - {\sqrt[3]{x}}^{1 + 1}$

Step 3.4.4

Add $1$ and $1$ .

$2 x \sqrt[3]{7} - {\sqrt[3]{x}}^{2}$

Step 3.5

Rewrite ${\sqrt[3]{x}}^{2}$ as $\sqrt[3]{x^{2}}$ .

$2 x \sqrt[3]{7} - \sqrt[3]{x^{2}}$