Basic Math Examples

$\frac{5 \sqrt[3]{10 y^{2}}}{3 \sqrt[3]{4 y^{2}}}$

Step 1

Combine $\sqrt[3]{10 y^{2}}$ and $\sqrt[3]{4 y^{2}}$ into a single radical.

$\frac{5 \sqrt[3]{\frac{10 y^{2}}{4 y^{2}}}}{3}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $10$ and $4$ .

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Step 2.1.1

Factor $2$ out of $10 y^{2}$ .

$\frac{5 \sqrt[3]{\frac{2 (5 y^{2})}{4 y^{2}}}}{3}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $2$ out of $4 y^{2}$ .

$\frac{5 \sqrt[3]{\frac{2 (5 y^{2})}{2 (2 y^{2})}}}{3}$

Step 2.1.2.2

Cancel the common factor.

$\frac{5 \sqrt[3]{\frac{2 (5 y^{2})}{2 (2 y^{2})}}}{3}$

Step 2.1.2.3

Rewrite the expression.

$\frac{5 \sqrt[3]{\frac{5 y^{2}}{2 y^{2}}}}{3}$

Step 2.2

Cancel the common factor of $y^{2}$ .

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Step 2.2.1

Cancel the common factor.

$\frac{5 \sqrt[3]{\frac{5 y^{2}}{2 y^{2}}}}{3}$

Step 2.2.2

Rewrite the expression.

$\frac{5 \sqrt[3]{\frac{5}{2}}}{3}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $\sqrt[3]{\frac{5}{2}}$ as $\frac{\sqrt[3]{5}}{\sqrt[3]{2}}$ .

$\frac{5 \frac{\sqrt[3]{5}}{\sqrt[3]{2}}}{3}$

Step 3.2

Multiply $\frac{\sqrt[3]{5}}{\sqrt[3]{2}}$ by $\frac{{\sqrt[3]{2}}^{2}}{{\sqrt[3]{2}}^{2}}$ .

$\frac{5 (\frac{\sqrt[3]{5}}{\sqrt[3]{2}} \cdot \frac{{\sqrt[3]{2}}^{2}}{{\sqrt[3]{2}}^{2}})}{3}$

Step 3.3

Combine and simplify the denominator.

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Step 3.3.1

Multiply $\frac{\sqrt[3]{5}}{\sqrt[3]{2}}$ by $\frac{{\sqrt[3]{2}}^{2}}{{\sqrt[3]{2}}^{2}}$ .

$\frac{5 \frac{\sqrt[3]{5} {\sqrt[3]{2}}^{2}}{\sqrt[3]{2} {\sqrt[3]{2}}^{2}}}{3}$

Step 3.3.2

Raise $\sqrt[3]{2}$ to the power of $1$ .

$\frac{5 \frac{\sqrt[3]{5} {\sqrt[3]{2}}^{2}}{{\sqrt[3]{2}}^{1} {\sqrt[3]{2}}^{2}}}{3}$

Step 3.3.3

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

$\frac{5 \frac{\sqrt[3]{5} {\sqrt[3]{2}}^{2}}{{\sqrt[3]{2}}^{1 + 2}}}{3}$

Step 3.3.4

Add $1$ and $2$ .

$\frac{5 \frac{\sqrt[3]{5} {\sqrt[3]{2}}^{2}}{{\sqrt[3]{2}}^{3}}}{3}$

Step 3.3.5

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

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Step 3.3.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2}$ as $2^{\frac{1}{3}}$ .

$\frac{5 \frac{\sqrt[3]{5} {\sqrt[3]{2}}^{2}}{{(2^{\frac{1}{3}})}^{3}}}{3}$

Step 3.3.5.2

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

$\frac{5 \frac{\sqrt[3]{5} {\sqrt[3]{2}}^{2}}{2^{\frac{1}{3} \cdot 3}}}{3}$

Step 3.3.5.3

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

$\frac{5 \frac{\sqrt[3]{5} {\sqrt[3]{2}}^{2}}{2^{\frac{3}{3}}}}{3}$

Step 3.3.5.4

Cancel the common factor of $3$ .

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Step 3.3.5.4.1

Cancel the common factor.

$\frac{5 \frac{\sqrt[3]{5} {\sqrt[3]{2}}^{2}}{2^{\frac{3}{3}}}}{3}$

Step 3.3.5.4.2

Rewrite the expression.

$\frac{5 \frac{\sqrt[3]{5} {\sqrt[3]{2}}^{2}}{2^{1}}}{3}$

Step 3.3.5.5

Evaluate the exponent.

$\frac{5 \frac{\sqrt[3]{5} {\sqrt[3]{2}}^{2}}{2}}{3}$

Step 3.4

Simplify the numerator.

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Step 3.4.1

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

$\frac{5 \frac{\sqrt[3]{5} \sqrt[3]{2^{2}}}{2}}{3}$

Step 3.4.2

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

$\frac{5 \frac{\sqrt[3]{5} \sqrt[3]{4}}{2}}{3}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Combine using the product rule for radicals.

$\frac{5 \frac{\sqrt[3]{5 \cdot 4}}{2}}{3}$

Step 3.5.2

Multiply $5$ by $4$ .

$\frac{5 \frac{\sqrt[3]{20}}{2}}{3}$

Step 4

Combine $5$ and $\frac{\sqrt[3]{20}}{2}$ .

$\frac{\frac{5 \sqrt[3]{20}}{2}}{3}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{5 \sqrt[3]{20}}{2} \cdot \frac{1}{3}$

Step 6

Multiply $\frac{5 \sqrt[3]{20}}{2} \cdot \frac{1}{3}$ .

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Step 6.1

Multiply $\frac{5 \sqrt[3]{20}}{2}$ by $\frac{1}{3}$ .

$\frac{5 \sqrt[3]{20}}{2 \cdot 3}$

Step 6.2

Multiply $2$ by $3$ .

$\frac{5 \sqrt[3]{20}}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{5 \sqrt[3]{20}}{6}$

Decimal Form:

$2.26201468 \dots$