Simplify ( square root of x^3y^2)/( square root of 9x^7)

$\frac{\sqrt{x^{3} y^{2}}}{\sqrt{9 x^{7}}}$

Step 1

Combine $\sqrt{x^{3} y^{2}}$ and $\sqrt{9 x^{7}}$ into a single radical.

$\sqrt{\frac{x^{3} y^{2}}{9 x^{7}}}$

Step 2

Reduce the expression $\frac{x^{3} y^{2}}{9 x^{7}}$ by cancelling the common factors.

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

$\sqrt{\frac{x^{3} (y^{2})}{9 x^{7}}}$

Factor $x^{3}$ out of $9 x^{7}$ .

$\sqrt{\frac{x^{3} (y^{2})}{x^{3} (9 x^{4})}}$

Cancel the common factor.

$\sqrt{\frac{x^{3} y^{2}}{x^{3} (9 x^{4})}}$

Rewrite the expression.

$\sqrt{\frac{y^{2}}{9 x^{4}}}$

Step 3

Rewrite $9 x^{4}$ as ${(3 x^{2})}^{2}$ .

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

Step 4

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

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

Step 5

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

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