Algebra Examples

$\sqrt[3]{\sqrt{243 x^{12}}}$

Step 1

Rewrite $243 x^{12}$ as ${(9 x^{6})}^{2} \cdot 3$ .

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Step 1.1

Factor $81$ out of $243$ .

$\sqrt[3]{\sqrt{81 (3) x^{12}}}$

Step 1.2

Rewrite $81$ as $9^{2}$ .

$\sqrt[3]{\sqrt{9^{2} \cdot 3 x^{12}}}$

Step 1.3

Rewrite $x^{12}$ as ${(x^{6})}^{2}$ .

$\sqrt[3]{\sqrt{9^{2} \cdot 3 {(x^{6})}^{2}}}$

Step 1.4

Move $3$ .

$\sqrt[3]{\sqrt{9^{2} {(x^{6})}^{2} \cdot 3}}$

Step 1.5

Rewrite $9^{2} {(x^{6})}^{2}$ as ${(9 x^{6})}^{2}$ .

$\sqrt[3]{\sqrt{{(9 x^{6})}^{2} \cdot 3}}$

Step 2

Pull terms out from under the radical.

$\sqrt[3]{| 9 x^{6} | \sqrt{3}}$

Step 3

Remove non-negative terms from the absolute value.

$\sqrt[3]{9 x^{6} \sqrt{3}}$

Step 4

Rewrite $9 x^{6} \sqrt{3}$ as ${(x^{2})}^{3} \cdot (9 \sqrt{3})$ .

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Step 4.1

Rewrite $x^{6}$ as ${(x^{2})}^{3}$ .

$\sqrt[3]{9 {(x^{2})}^{3} \sqrt{3}}$

Step 4.2

Reorder $9$ and ${(x^{2})}^{3}$ .

$\sqrt[3]{{(x^{2})}^{3} \cdot 9 \sqrt{3}}$

Step 4.3

Add parentheses.

$\sqrt[3]{{(x^{2})}^{3} \cdot (9 \sqrt{3})}$

Step 5

Pull terms out from under the radical.

$x^{2} \sqrt[3]{9 \sqrt{3}}$