Simplify square root of (272p^9)/(324q^2)

$\sqrt{\frac{272 p^{9}}{324 q^{2}}}$

Step 1

Reduce the expression $\frac{272 p^{9}}{324 q^{2}}$ by cancelling the common factors.

Factor $4$ out of $272 p^{9}$ .

$\sqrt{\frac{4 (68 p^{9})}{324 q^{2}}}$

Factor $4$ out of $324 q^{2}$ .

$\sqrt{\frac{4 (68 p^{9})}{4 (81 q^{2})}}$

Cancel the common factor.

$\sqrt{\frac{4 (68 p^{9})}{4 (81 q^{2})}}$

Rewrite the expression.

$\sqrt{\frac{68 p^{9}}{81 q^{2}}}$

Step 2

Rewrite $\frac{68 p^{9}}{81 q^{2}}$ as ${(\frac{2 p^{4}}{9 q})}^{2} (17 p)$ .

Factor the perfect power ${(2 p^{4})}^{2}$ out of $68 p^{9}$ .

$\sqrt{\frac{{(2 p^{4})}^{2} \cdot (17 p)}{81 q^{2}}}$

Factor the perfect power ${(9 q)}^{2}$ out of $81 q^{2}$ .

$\sqrt{\frac{{(2 p^{4})}^{2} \cdot (17 p)}{{(9 q)}^{2} \cdot 1}}$

Rearrange the fraction $\frac{{(2 p^{4})}^{2} \cdot (17 p)}{{(9 q)}^{2} \cdot 1}$ .

$\sqrt{{(\frac{2 p^{4}}{9 q})}^{2} (17 p)}$

Step 3

Pull terms out from under the radical.

$\frac{2 p^{4}}{9 q} \sqrt{17 p}$

Step 4

Combine $\frac{2 p^{4}}{9 q}$ and $\sqrt{17 p}$ .

$\frac{2 p^{4} \sqrt{17 p}}{9 q}$