Pre-Algebra Examples

$\sqrt{\frac{z^{6}}{64 x^{6} z^{8}}}$

Step 1

Reduce the expression $\frac{z^{6}}{64 x^{6} z^{8}}$ by cancelling the common factors.

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Step 1.1

Multiply by $1$ .

$\sqrt{\frac{z^{6} \cdot 1}{64 x^{6} z^{8}}}$

Step 1.2

Factor $z^{6}$ out of $64 x^{6} z^{8}$ .

$\sqrt{\frac{z^{6} \cdot 1}{z^{6} (64 x^{6} z^{2})}}$

Step 1.3

Cancel the common factor.

$\sqrt{\frac{z^{6} \cdot 1}{z^{6} (64 x^{6} z^{2})}}$

Step 1.4

Rewrite the expression.

$\sqrt{\frac{1}{64 x^{6} z^{2}}}$

Step 2

Rewrite $1$ as $1^{2}$ .

$\sqrt{\frac{1^{2}}{64 x^{6} z^{2}}}$

Step 3

Rewrite $64 x^{6} z^{2}$ as ${(8 x^{3} z)}^{2}$ .

$\sqrt{\frac{1^{2}}{{(8 x^{3} z)}^{2}}}$

Step 4

Rewrite $\frac{1^{2}}{{(8 x^{3} z)}^{2}}$ as ${(\frac{1}{8 x^{3} z})}^{2}$ .

$\sqrt{{(\frac{1}{8 x^{3} z})}^{2}}$

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$\frac{1}{8 x^{3} z}$