Algebra Examples

$\frac{1}{5} \sqrt{75 x y^{2} z^{3}}$

Step 1

Rewrite $75 x y^{2} z^{3}$ as ${(5 y z)}^{2} \cdot (3 x z)$ .

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Step 1.1

Factor $25$ out of $75$ .

$\frac{1}{5} \cdot \sqrt{25 (3) x y^{2} z^{3}}$

Step 1.2

Rewrite $25$ as $5^{2}$ .

$\frac{1}{5} \cdot \sqrt{5^{2} \cdot 3 x y^{2} z^{3}}$

Step 1.3

Factor out $z^{2}$ .

$\frac{1}{5} \cdot \sqrt{5^{2} \cdot 3 x y^{2} (z^{2} z)}$

Step 1.4

Move $x$ .

$\frac{1}{5} \cdot \sqrt{5^{2} \cdot 3 y^{2} z^{2} x z}$

Step 1.5

Move $3$ .

$\frac{1}{5} \cdot \sqrt{5^{2} y^{2} z^{2} \cdot 3 x z}$

Step 1.6

Rewrite $5^{2} y^{2} z^{2}$ as ${(5 y z)}^{2}$ .

$\frac{1}{5} \cdot \sqrt{{(5 y z)}^{2} \cdot 3 x z}$

Step 1.7

Add parentheses.

$\frac{1}{5} \cdot \sqrt{{(5 y z)}^{2} \cdot 3 (x z)}$

Step 1.8

Add parentheses.

$\frac{1}{5} \cdot \sqrt{{(5 y z)}^{2} \cdot (3 x z)}$

Step 2

Pull terms out from under the radical.

$\frac{1}{5} \cdot (5 y z \sqrt{3 x z})$

Step 3

Cancel the common factor of $5$ .

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Step 3.1

Factor $5$ out of $5 y z \sqrt{3 x z}$ .

$\frac{1}{5} \cdot (5 (y z \sqrt{3 x z}))$

Step 3.2

Cancel the common factor.

$\frac{1}{5} \cdot (5 (y z \sqrt{3 x z}))$

Step 3.3

Rewrite the expression.

$y z \sqrt{3 x z}$