Algebra Examples

$\sqrt{18 x^{4} y^{6} z^{8}}$

Step 1

Rewrite $18 x^{4} y^{6} z^{8}$ as ${(3 x^{2} y^{3} z^{4})}^{2} \cdot 2$ .

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Step 1.1

Factor $9$ out of $18$ .

$\sqrt{9 (2) x^{4} y^{6} z^{8}}$

Step 1.2

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 2 x^{4} y^{6} z^{8}}$

Step 1.3

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

$\sqrt{3^{2} \cdot 2 {(x^{2})}^{2} y^{6} z^{8}}$

Step 1.4

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

$\sqrt{3^{2} \cdot 2 {(x^{2})}^{2} {(y^{3})}^{2} z^{8}}$

Step 1.5

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

$\sqrt{3^{2} \cdot 2 {(x^{2})}^{2} {(y^{3})}^{2} {(z^{4})}^{2}}$

Step 1.6

Move $2$ .

$\sqrt{3^{2} {(x^{2})}^{2} {(y^{3})}^{2} {(z^{4})}^{2} \cdot 2}$

Step 1.7

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

$\sqrt{{(3 x^{2} y^{3} z^{4})}^{2} \cdot 2}$

Step 2

Pull terms out from under the radical.

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

Step 3

Remove non-negative terms from the absolute value.

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