Algebra Examples

$\sqrt[4]{81 x^{8} y^{6}}$

Step 1

Rewrite $81 x^{8} y^{6}$ as ${(3 x^{2} y)}^{4} y^{2}$ .

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Step 1.1

Rewrite $81$ as $3^{4}$ .

$\sqrt[4]{3^{4} x^{8} y^{6}}$

Step 1.2

Rewrite $x^{8}$ as ${(x^{2})}^{4}$ .

$\sqrt[4]{3^{4} {(x^{2})}^{4} y^{6}}$

Step 1.3

Factor out $y^{4}$ .

$\sqrt[4]{3^{4} {(x^{2})}^{4} (y^{4} y^{2})}$

Step 1.4

Rewrite $3^{4} {(x^{2})}^{4} y^{4}$ as ${(3 x^{2} y)}^{4}$ .

$\sqrt[4]{{(3 x^{2} y)}^{4} y^{2}}$

Step 2

Pull terms out from under the radical.

$| 3 x^{2} y | \sqrt[4]{y^{2}}$

Step 3

Remove non-negative terms from the absolute value.

$3 x^{2} | y | \sqrt[4]{y^{2}}$

Step 4

Rewrite $\sqrt[4]{y^{2}}$ as $\sqrt{\sqrt{y^{2}}}$ .

$3 x^{2} | y | \sqrt{\sqrt{y^{2}}}$

Step 5

Pull terms out from under the radical.

$3 x^{2} | y | \sqrt{| y |}$