Simplify the Radical Expression square root of (28x^3y^2z)/(7xy^2)

$\sqrt{\frac{28 x^{3} y^{2} z}{7 x y^{2}}}$

Step 1

Reduce the expression $\frac{28 x^{3} y^{2} z}{7 x y^{2}}$ by cancelling the common factors.

Factor $7$ out of $28 x^{3} y^{2} z$ .

$\sqrt{\frac{7 (4 x^{3} y^{2} z)}{7 x y^{2}}}$

Factor $7$ out of $7 x y^{2}$ .

$\sqrt{\frac{7 (4 x^{3} y^{2} z)}{7 (x y^{2})}}$

Cancel the common factor.

$\sqrt{\frac{7 (4 x^{3} y^{2} z)}{7 (x y^{2})}}$

Rewrite the expression.

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

Step 2

Cancel the common factor of $x^{3}$ and $x$ .

Factor $x$ out of $4 x^{3} y^{2} z$ .

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

Cancel the common factors.

Factor $x$ out of $x y^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\sqrt{\frac{4 x^{2} y^{2} z}{y^{2}}}$

Step 3

Cancel the common factor of $y^{2}$ .

Cancel the common factor.

$\sqrt{\frac{4 x^{2} y^{2} z}{y^{2}}}$

Divide $4 x^{2} z$ by $1$ .

$\sqrt{4 x^{2} z}$

Step 4

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

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} x^{2} z}$

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

$\sqrt{{(2 x)}^{2} z}$

Step 5

Pull terms out from under the radical.

$| 2 x | \sqrt{z}$

Step 6

Remove non-negative terms from the absolute value.

$2 | x | \sqrt{z}$