Algebra Examples

$\sqrt{\sqrt[3]{x^{10}}}$

Step 1

Rewrite $x^{10}$ as ${(x^{3})}^{3} x$ .

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Step 1.1

Factor out $x^{9}$ .

$\sqrt{\sqrt[3]{x^{9} x}}$

Step 1.2

Rewrite $x^{9}$ as ${(x^{3})}^{3}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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Step 3.1

Factor out $x^{2}$ .

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

Step 3.2

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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