Simplify ( square root of 75x^5)/( square root of 12xy^2)

$\frac{\sqrt{75 x^{5}}}{\sqrt{12 x y^{2}}}$

Step 1

Combine $\sqrt{75 x^{5}}$ and $\sqrt{12 x y^{2}}$ into a single radical.

$\sqrt{\frac{75 x^{5}}{12 x y^{2}}}$

Step 2

Reduce the expression $\frac{75 x^{5}}{12 x y^{2}}$ by cancelling the common factors.

Factor $3$ out of $75 x^{5}$ .

$\sqrt{\frac{3 (25 x^{5})}{12 x y^{2}}}$

Factor $3$ out of $12 x y^{2}$ .

$\sqrt{\frac{3 (25 x^{5})}{3 (4 x y^{2})}}$

Cancel the common factor.

$\sqrt{\frac{3 (25 x^{5})}{3 (4 x y^{2})}}$

Rewrite the expression.

$\sqrt{\frac{25 x^{5}}{4 x y^{2}}}$

Step 3

Cancel the common factor of $x^{5}$ and $x$ .

Factor $x$ out of $25 x^{5}$ .

$\sqrt{\frac{x (25 x^{4})}{4 x y^{2}}}$

Cancel the common factors.

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

$\sqrt{\frac{x (25 x^{4})}{x (4 y^{2})}}$

Cancel the common factor.

$\sqrt{\frac{x (25 x^{4})}{x (4 y^{2})}}$

Rewrite the expression.

$\sqrt{\frac{25 x^{4}}{4 y^{2}}}$

Step 4

Rewrite $25 x^{4}$ as ${(5 x^{2})}^{2}$ .

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

Step 5

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

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

Step 6

Rewrite $\frac{{(5 x^{2})}^{2}}{{(2 y)}^{2}}$ as ${(\frac{5 x^{2}}{2 y})}^{2}$ .

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

Step 7

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

$\frac{5 x^{2}}{2 y}$