Algebra Examples

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

Step 1

Rewrite the expression using the least common index of $6$ .

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Step 1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{5}$ as $5^{\frac{1}{3}}$ .

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

Step 1.2

Rewrite $5^{\frac{1}{3}}$ as $5^{\frac{2}{6}}$ .

$2 (5^{\frac{2}{6}} \sqrt{3})$

Step 1.3

Rewrite $5^{\frac{2}{6}}$ as $\sqrt[6]{5^{2}}$ .

$2 (\sqrt[6]{5^{2}} \sqrt{3})$

Step 1.4

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

$2 (\sqrt[6]{5^{2}} \cdot 3^{\frac{1}{2}})$

Step 1.5

Rewrite $3^{\frac{1}{2}}$ as $3^{\frac{3}{6}}$ .

$2 (\sqrt[6]{5^{2}} \cdot 3^{\frac{3}{6}})$

Step 1.6

Rewrite $3^{\frac{3}{6}}$ as $\sqrt[6]{3^{3}}$ .

$2 (\sqrt[6]{5^{2}} \sqrt[6]{3^{3}})$

Step 2

Combine using the product rule for radicals.

$2 \sqrt[6]{5^{2} \cdot 3^{3}}$

Step 3

Raise $5$ to the power of $2$ .

$2 \sqrt[6]{25 \cdot 3^{3}}$

Step 4

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

$2 \sqrt[6]{25 \cdot 27}$

Step 5

Multiply $25$ by $27$ .

$2 \sqrt[6]{675}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt[6]{675}$

Decimal Form:

$5.92353043 \dots$