Simplify square root of (xy^2)/(16y^5)

$\sqrt{\frac{x y^{2}}{16 y^{5}}}$

Step 1

Reduce the expression $\frac{x y^{2}}{16 y^{5}}$ by cancelling the common factors.

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

$\sqrt{\frac{y^{2} x}{16 y^{5}}}$

Factor $y^{2}$ out of $16 y^{5}$ .

$\sqrt{\frac{y^{2} x}{y^{2} (16 y^{3})}}$

Cancel the common factor.

$\sqrt{\frac{y^{2} x}{y^{2} (16 y^{3})}}$

Rewrite the expression.

$\sqrt{\frac{x}{16 y^{3}}}$

Step 2

Rewrite $\frac{x}{16 y^{3}}$ as ${(\frac{1}{4 y})}^{2} \frac{x}{y}$ .

Factor the perfect power $1^{2}$ out of $x$ .

$\sqrt{\frac{1^{2} x}{16 y^{3}}}$

Factor the perfect power ${(4 y)}^{2}$ out of $16 y^{3}$ .

$\sqrt{\frac{1^{2} x}{{(4 y)}^{2} y}}$

Rearrange the fraction $\frac{1^{2} x}{{(4 y)}^{2} y}$ .

$\sqrt{{(\frac{1}{4 y})}^{2} \frac{x}{y}}$

Step 3

Pull terms out from under the radical.

$\frac{1}{4 y} \sqrt{\frac{x}{y}}$

Step 4

Rewrite $\sqrt{\frac{x}{y}}$ as $\frac{\sqrt{x}}{\sqrt{y}}$ .

$\frac{1}{4 y} \cdot \frac{\sqrt{x}}{\sqrt{y}}$

Step 5

Multiply $\frac{\sqrt{x}}{\sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

$\frac{1}{4 y} (\frac{\sqrt{x}}{\sqrt{y}} \cdot \frac{\sqrt{y}}{\sqrt{y}})$

Step 6

Combine and simplify the denominator.

Multiply $\frac{\sqrt{x}}{\sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

$\frac{1}{4 y} \cdot \frac{\sqrt{x} \sqrt{y}}{\sqrt{y} \sqrt{y}}$

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

$\frac{1}{4 y} \cdot \frac{\sqrt{x} \sqrt{y}}{{\sqrt{y}}^{1} \sqrt{y}}$

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

$\frac{1}{4 y} \cdot \frac{\sqrt{x} \sqrt{y}}{{\sqrt{y}}^{1} {\sqrt{y}}^{1}}$

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

$\frac{1}{4 y} \cdot \frac{\sqrt{x} \sqrt{y}}{{\sqrt{y}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{1}{4 y} \cdot \frac{\sqrt{x} \sqrt{y}}{{\sqrt{y}}^{2}}$

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

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

$\frac{1}{4 y} \cdot \frac{\sqrt{x} \sqrt{y}}{{(y^{\frac{1}{2}})}^{2}}$

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

$\frac{1}{4 y} \cdot \frac{\sqrt{x} \sqrt{y}}{y^{\frac{1}{2} \cdot 2}}$

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

$\frac{1}{4 y} \cdot \frac{\sqrt{x} \sqrt{y}}{y^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{1}{4 y} \cdot \frac{\sqrt{x} \sqrt{y}}{y^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{1}{4 y} \cdot \frac{\sqrt{x} \sqrt{y}}{y^{1}}$

Simplify.

$\frac{1}{4 y} \cdot \frac{\sqrt{x} \sqrt{y}}{y}$

Step 7

Combine using the product rule for radicals.

$\frac{1}{4 y} \cdot \frac{\sqrt{x y}}{y}$

Step 8

Multiply $\frac{1}{4 y} \cdot \frac{\sqrt{x y}}{y}$ .

Multiply $\frac{1}{4 y}$ by $\frac{\sqrt{x y}}{y}$ .

$\frac{\sqrt{x y}}{4 y \cdot y}$

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

$\frac{\sqrt{x y}}{4 (y^{1} y)}$

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

$\frac{\sqrt{x y}}{4 (y^{1} y^{1})}$

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

$\frac{\sqrt{x y}}{4 y^{1 + 1}}$

Add $1$ and $1$ .

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

Simplify square root of (xy^2)/(16y^5)

Related Questions

Support LCMGCF.com by disabling your adblocker.