Simplify square root of (9x^9)/(75x^5)

$\sqrt{\frac{9 x^{9}}{75 x^{5}}}$

Step 1

Reduce the expression $\frac{9 x^{9}}{75 x^{5}}$ by cancelling the common factors.

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

$\sqrt{\frac{3 (3 x^{9})}{75 x^{5}}}$

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

$\sqrt{\frac{3 (3 x^{9})}{3 (25 x^{5})}}$

Cancel the common factor.

$\sqrt{\frac{3 (3 x^{9})}{3 (25 x^{5})}}$

Rewrite the expression.

$\sqrt{\frac{3 x^{9}}{25 x^{5}}}$

Step 2

Cancel the common factor of $x^{9}$ and $x^{5}$ .

Factor $x^{5}$ out of $3 x^{9}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

$\sqrt{\frac{3 x^{4}}{25}}$

Step 3

Rewrite $\frac{3 x^{4}}{25}$ as ${(\frac{x^{2}}{5})}^{2} \cdot 3$ .

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

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

Factor the perfect power $5^{2}$ out of $25$ .

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

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

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

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