Algebra Examples

$\sqrt{x^{3}} \sqrt[3]{y}$

Step 1

Factor out $x^{2}$ .

$\sqrt{x^{2} x} \sqrt[3]{y}$

Step 2

Pull terms out from under the radical.

$x \sqrt{x} \sqrt[3]{y}$

Step 3

Multiply $x \sqrt{x} \sqrt[3]{y}$ .

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Step 3.1

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

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Step 3.1.1

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

$x (y^{\frac{1}{3}} \sqrt{x})$

Step 3.1.2

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

$x (y^{\frac{2}{6}} \sqrt{x})$

Step 3.1.3

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

$x (\sqrt[6]{y^{2}} \sqrt{x})$

Step 3.1.4

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

$x (\sqrt[6]{y^{2}} x^{\frac{1}{2}})$

Step 3.1.5

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

$x (\sqrt[6]{y^{2}} x^{\frac{3}{6}})$

Step 3.1.6

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

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

Step 3.2

Combine using the product rule for radicals.

$x \sqrt[6]{y^{2} x^{3}}$