Simplify square root of (20x^3y^2)/(9xz^3)

$\sqrt{\frac{20 x^{3} y^{2}}{9 x z^{3}}}$

Reduce the expression $\frac{20 x^{3} y^{2}}{9 x z^{3}}$ by cancelling the common factors.

Factor $x$ out of $20 x^{3} y^{2}$ .

$\sqrt{\frac{x (20 x^{2} y^{2})}{9 x z^{3}}}$

Factor $x$ out of $9 x z^{3}$ .

$\sqrt{\frac{x (20 x^{2} y^{2})}{x (9 z^{3})}}$

Cancel the common factor.

$\sqrt{\frac{x (20 x^{2} y^{2})}{x (9 z^{3})}}$

Rewrite the expression.

$\sqrt{\frac{20 x^{2} y^{2}}{9 z^{3}}}$

Rewrite $\frac{20 x^{2} y^{2}}{9 z^{3}}$ as ${(\frac{2 x y}{3 z})}^{2} \frac{5}{z}$ .

Factor the perfect power ${(2 x y)}^{2}$ out of $20 x^{2} y^{2}$ .

$\sqrt{\frac{{(2 x y)}^{2} \cdot 5}{9 z^{3}}}$

Factor the perfect power ${(3 z)}^{2}$ out of $9 z^{3}$ .

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

Rearrange the fraction $\frac{{(2 x y)}^{2} \cdot 5}{{(3 z)}^{2} z}$ .

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

Pull terms out from under the radical.

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

Rewrite $\sqrt{\frac{5}{z}}$ as $\frac{\sqrt{5}}{\sqrt{z}}$ .

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

Multiply $\frac{\sqrt{5}}{\sqrt{z}}$ by $\frac{\sqrt{z}}{\sqrt{z}}$ .

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

Combine and simplify the denominator.

Multiply $\frac{\sqrt{5}}{\sqrt{z}}$ by $\frac{\sqrt{z}}{\sqrt{z}}$ .

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

Raise $\sqrt{z}$ to the power of $1$ .

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

Raise $\sqrt{z}$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

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

Rewrite ${\sqrt{z}}^{2}$ as $z$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{z}$ as $z^{\frac{1}{2}}$ .

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

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Combine using the product rule for radicals.

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

Multiply $\frac{2 x y}{3 z} \cdot \frac{\sqrt{5 z}}{z}$ .

Multiply $\frac{2 x y}{3 z}$ by $\frac{\sqrt{5 z}}{z}$ .

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

Raise $z$ to the power of $1$ .

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

Raise $z$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

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

Simplify square root of (20x^3y^2)/(9xz^3)

Related Questions

Support LCMGCF.com by disabling your adblocker.