Finite Math Examples

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

Step 1

Rewrite the expression using the least common index of $12$ .

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Step 1.1

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

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

Step 1.2

Rewrite $2^{\frac{1}{3}}$ as $2^{\frac{4}{12}}$ .

$2^{\frac{4}{12}} \sqrt[4]{3}$

Step 1.3

Rewrite $2^{\frac{4}{12}}$ as $\sqrt[12]{2^{4}}$ .

$\sqrt[12]{2^{4}} \sqrt[4]{3}$

Step 1.4

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{3}$ as $3^{\frac{1}{4}}$ .

$\sqrt[12]{2^{4}} \cdot 3^{\frac{1}{4}}$

Step 1.5

Rewrite $3^{\frac{1}{4}}$ as $3^{\frac{3}{12}}$ .

$\sqrt[12]{2^{4}} \cdot 3^{\frac{3}{12}}$

Step 1.6

Rewrite $3^{\frac{3}{12}}$ as $\sqrt[12]{3^{3}}$ .

$\sqrt[12]{2^{4}} \sqrt[12]{3^{3}}$

Step 2

Combine using the product rule for radicals.

$\sqrt[12]{2^{4} \cdot 3^{3}}$

Step 3

Raise $2$ to the power of $4$ .

$\sqrt[12]{16 \cdot 3^{3}}$

Step 4

Raise $3$ to the power of $3$ .

$\sqrt[12]{16 \cdot 27}$

Step 5

Multiply $16$ by $27$ .

$\sqrt[12]{432}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\sqrt[12]{432}$

Decimal Form:

$1.65814935 \dots$