Simplify square root of (4x^2)/(3y)

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

Step 1

Rewrite $\sqrt{\frac{4 x^{2}}{3 y}}$ as $\frac{\sqrt{4 x^{2}}}{\sqrt{3 y}}$ .

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

Step 2

Simplify the numerator.

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

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

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

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

Step 3

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

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

Step 4

Combine and simplify the denominator.

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

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

Raise $\sqrt{3 y}$ to the power of $1$ .

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

Raise $\sqrt{3 y}$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

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

Rewrite ${\sqrt{3 y}}^{2}$ as $3 y$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 y}$ as ${(3 y)}^{\frac{1}{2}}$ .

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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