Basic Math Examples

$\sqrt[3]{5} \cdot \sqrt{5}$

Step 1

Multiply $\sqrt[3]{5} \sqrt{5}$ .

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Step 1.1

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

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Step 1.1.1

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

$5^{\frac{1}{3}} \sqrt{5}$

Step 1.1.2

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

$5^{\frac{2}{6}} \sqrt{5}$

Step 1.1.3

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

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

Step 1.1.4

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

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

Step 1.1.5

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

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

Step 1.1.6

Rewrite $5^{\frac{3}{6}}$ as $\sqrt[6]{5^{3}}$ .

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

Step 1.2

Combine using the product rule for radicals.

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

Step 1.3

Multiply $5^{2}$ by $5^{3}$ by adding the exponents.

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Step 1.3.1

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

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

Step 1.3.2

Add $2$ and $3$ .

$\sqrt[6]{5^{5}}$

Step 2

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

$\sqrt[6]{3125}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt[6]{3125}$

Decimal Form:

$3.82362245 \dots$