Algebra Examples

$\sqrt[3]{\frac{375}{4}}$

Step 1

Rewrite $\sqrt[3]{\frac{375}{4}}$ as $\frac{\sqrt[3]{375}}{\sqrt[3]{4}}$ .

$\frac{\sqrt[3]{375}}{\sqrt[3]{4}}$

Step 2

Multiply to rationalize the numerator.

$\frac{\sqrt[3]{375} {\sqrt[3]{375}}^{2}}{\sqrt[3]{4} {\sqrt[3]{375}}^{2}}$

Step 3

Simplify.

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Step 3.1

Raise $\sqrt[3]{375}$ to the power of $1$ .

$\frac{{\sqrt[3]{375}}^{1} {\sqrt[3]{375}}^{2}}{\sqrt[3]{4} {\sqrt[3]{375}}^{2}}$

Step 3.2

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

$\frac{{\sqrt[3]{375}}^{1 + 2}}{\sqrt[3]{4} {\sqrt[3]{375}}^{2}}$

Step 3.3

Add $1$ and $2$ .

$\frac{{\sqrt[3]{375}}^{3}}{\sqrt[3]{4} {\sqrt[3]{375}}^{2}}$

Step 3.4

Rewrite ${\sqrt[3]{375}}^{3}$ as $375$ .

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Step 3.4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{375}$ as $375^{\frac{1}{3}}$ .

$\frac{{(375^{\frac{1}{3}})}^{3}}{\sqrt[3]{4} {\sqrt[3]{375}}^{2}}$

Step 3.4.2

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

$\frac{375^{\frac{1}{3} \cdot 3}}{\sqrt[3]{4} {\sqrt[3]{375}}^{2}}$

Step 3.4.3

Combine $\frac{1}{3}$ and $3$ .

$\frac{375^{\frac{3}{3}}}{\sqrt[3]{4} {\sqrt[3]{375}}^{2}}$

Step 3.4.4

Cancel the common factor of $3$ .

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Step 3.4.4.1

Cancel the common factor.

$\frac{375^{\frac{3}{3}}}{\sqrt[3]{4} {\sqrt[3]{375}}^{2}}$

Step 3.4.4.2

Rewrite the expression.

$\frac{375^{1}}{\sqrt[3]{4} {\sqrt[3]{375}}^{2}}$

Step 3.4.5

Evaluate the exponent.

$\frac{375}{\sqrt[3]{4} {\sqrt[3]{375}}^{2}}$

Step 3.5

Start simplifying.

$\frac{375}{\sqrt[3]{4} \sqrt[3]{375^{2}}}$

Step 3.6

Combine using the product rule for radicals.

$\frac{375}{\sqrt[3]{4 \cdot 375^{2}}}$

Step 3.7

Raise $375$ to the power of $2$ .

$\frac{375}{\sqrt[3]{4 \cdot 140625}}$

Step 3.8

Multiply $4$ by $140625$ .

$\frac{375}{\sqrt[3]{562500}}$

Step 3.9

Rewrite $562500$ as $25^{3} \cdot 36$ .

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Step 3.9.1

Factor $15625$ out of $562500$ .

$\frac{375}{\sqrt[3]{15625 (36)}}$

Step 3.9.2

Rewrite $15625$ as $25^{3}$ .

$\frac{375}{\sqrt[3]{25^{3} \cdot 36}}$

Step 3.10

Pull terms out from under the radical.

$\frac{375}{25 \sqrt[3]{36}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{375}{25 \sqrt[3]{36}}$

Decimal Form:

$4.54280148 \dots$