Simplify the Radical Expression square root of (45x^3y^4)/(16x^2)

$\sqrt{\frac{45 x^{3} y^{4}}{16 x^{2}}}$

Reduce the expression $\frac{45 x^{3} y^{4}}{16 x^{2}}$ by cancelling the common factors.

Factor $x^{2}$ out of $45 x^{3} y^{4}$ .

$\sqrt{\frac{x^{2} (45 x y^{4})}{16 x^{2}}}$

Factor $x^{2}$ out of $16 x^{2}$ .

$\sqrt{\frac{x^{2} (45 x y^{4})}{x^{2} \cdot 16}}$

Cancel the common factor.

$\sqrt{\frac{x^{2} (45 x y^{4})}{x^{2} \cdot 16}}$

Rewrite the expression.

$\sqrt{\frac{45 x y^{4}}{16}}$

Rewrite $\frac{45 x y^{4}}{16}$ as ${(\frac{3 y^{2}}{4})}^{2} (5 x)$ .

Factor the perfect power ${(3 y^{2})}^{2}$ out of $45 x y^{4}$ .

$\sqrt{\frac{{(3 y^{2})}^{2} \cdot (5 x)}{16}}$

Factor the perfect power $4^{2}$ out of $16$ .

$\sqrt{\frac{{(3 y^{2})}^{2} \cdot (5 x)}{4^{2} \cdot 1}}$

Rearrange the fraction $\frac{{(3 y^{2})}^{2} \cdot (5 x)}{4^{2} \cdot 1}$ .

$\sqrt{{(\frac{3 y^{2}}{4})}^{2} (5 x)}$

Pull terms out from under the radical.

$| \frac{3 y^{2}}{4} | \sqrt{5 x}$

Remove non-negative terms from the absolute value.

$\frac{3 y^{2}}{4} \sqrt{5 x}$

Combine $\frac{3 y^{2}}{4}$ and $\sqrt{5 x}$ .

$\frac{3 y^{2} \sqrt{5 x}}{4}$