Simplify square root of (3x^3)/(64x^2)

$\sqrt{\frac{3 x^{3}}{64 x^{2}}}$

Step 1

Reduce the expression $\frac{3 x^{3}}{64 x^{2}}$ by cancelling the common factors.

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

$\sqrt{\frac{x^{2} (3 x)}{64 x^{2}}}$

Factor $x^{2}$ out of $64 x^{2}$ .

$\sqrt{\frac{x^{2} (3 x)}{x^{2} \cdot 64}}$

Cancel the common factor.

$\sqrt{\frac{x^{2} (3 x)}{x^{2} \cdot 64}}$

Rewrite the expression.

$\sqrt{\frac{3 x}{64}}$

Step 2

Rewrite $\frac{3 x}{64}$ as ${(\frac{1}{8})}^{2} (3 x)$ .

Factor the perfect power $1^{2}$ out of $3 x$ .

$\sqrt{\frac{1^{2} (3 x)}{64}}$

Factor the perfect power $8^{2}$ out of $64$ .

$\sqrt{\frac{1^{2} (3 x)}{8^{2} \cdot 1}}$

Rearrange the fraction $\frac{1^{2} (3 x)}{8^{2} \cdot 1}$ .

$\sqrt{{(\frac{1}{8})}^{2} (3 x)}$

Step 3

Pull terms out from under the radical.

$\frac{1}{8} \sqrt{3 x}$

Step 4

Combine $\frac{1}{8}$ and $\sqrt{3 x}$ .

$\frac{\sqrt{3 x}}{8}$