Simplify square root of (27x^4)/(75y^2)

$\sqrt{\frac{27 x^{4}}{75 y^{2}}}$

Step 1

Reduce the expression $\frac{27 x^{4}}{75 y^{2}}$ by cancelling the common factors.

Factor $3$ out of $27 x^{4}$ .

$\sqrt{\frac{3 (9 x^{4})}{75 y^{2}}}$

Factor $3$ out of $75 y^{2}$ .

$\sqrt{\frac{3 (9 x^{4})}{3 (25 y^{2})}}$

Cancel the common factor.

$\sqrt{\frac{3 (9 x^{4})}{3 (25 y^{2})}}$

Rewrite the expression.

$\sqrt{\frac{9 x^{4}}{25 y^{2}}}$

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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