Basic Math Examples

$146 c^{3} = n (\sqrt[3]{1728})$

Step 1

Rewrite the equation as $n (\sqrt[3]{1728}) = 146 c^{3}$ .

$n (\sqrt[3]{1728}) = 146 c^{3}$

Step 2

Divide each term in $n (\sqrt[3]{1728}) = 146 c^{3}$ by $\sqrt[3]{1728}$ and simplify.

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Step 2.1

Divide each term in $n (\sqrt[3]{1728}) = 146 c^{3}$ by $\sqrt[3]{1728}$ .

$\frac{n \sqrt[3]{1728}}{\sqrt[3]{1728}} = \frac{146 c^{3}}{\sqrt[3]{1728}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $\sqrt[3]{1728}$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{n \sqrt[3]{1728}}{\sqrt[3]{1728}} = \frac{146 c^{3}}{\sqrt[3]{1728}}$

Step 2.2.1.2

Divide $n$ by $1$ .

$n = \frac{146 c^{3}}{\sqrt[3]{1728}}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify the denominator.

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Step 2.3.1.1

Rewrite $1728$ as $12^{3}$ .

$n = \frac{146 c^{3}}{\sqrt[3]{12^{3}}}$

Step 2.3.1.2

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

$n = \frac{146 c^{3}}{12}$

Step 2.3.2

Cancel the common factor of $146$ and $12$ .

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Step 2.3.2.1

Factor $2$ out of $146 c^{3}$ .

$n = \frac{2 (73 c^{3})}{12}$

Step 2.3.2.2

Cancel the common factors.

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Step 2.3.2.2.1

Factor $2$ out of $12$ .

$n = \frac{2 (73 c^{3})}{2 (6)}$

Step 2.3.2.2.2

Cancel the common factor.

$n = \frac{2 (73 c^{3})}{2 \cdot 6}$

Step 2.3.2.2.3

Rewrite the expression.

$n = \frac{73 c^{3}}{6}$