Simplify square root of (7x^2)/(9y^2)

$\sqrt{\frac{7 x^{2}}{9 y^{2}}}$

Step 1

Rewrite $\frac{7 x^{2}}{9 y^{2}}$ as ${(\frac{x}{3 y})}^{2} \cdot 7$ .

Factor the perfect power $x^{2}$ out of $7 x^{2}$ .

$\sqrt{\frac{x^{2} \cdot 7}{9 y^{2}}}$

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

$\sqrt{\frac{x^{2} \cdot 7}{{(3 y)}^{2} \cdot 1}}$

Rearrange the fraction $\frac{x^{2} \cdot 7}{{(3 y)}^{2} \cdot 1}$ .

$\sqrt{{(\frac{x}{3 y})}^{2} \cdot 7}$

Step 2

Pull terms out from under the radical.

$\frac{x}{3 y} \sqrt{7}$

Step 3

Combine $\frac{x}{3 y}$ and $\sqrt{7}$ .

$\frac{x \sqrt{7}}{3 y}$