Simplify the Radical Expression square root of (81x^4)/(9x^2)

$\sqrt{\frac{81 x^{4}}{9 x^{2}}}$

Step 1

Reduce the expression $\frac{81 x^{4}}{9 x^{2}}$ by cancelling the common factors.

Factor $9$ out of $81 x^{4}$ .

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

Factor $9$ out of $9 x^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Cancel the common factor of $x^{4}$ and $x^{2}$ .

Factor $x^{2}$ out of $9 x^{4}$ .

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

Cancel the common factors.

Multiply by $1$ .

$\sqrt{\frac{x^{2} (9 x^{2})}{x^{2} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x^{2} (9 x^{2})}{x^{2} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{9 x^{2}}{1}}$

Divide $9 x^{2}$ by $1$ .

$\sqrt{9 x^{2}}$

Step 3

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

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

Step 4

Pull terms out from under the radical.

$| 3 x |$

Step 5

Remove non-negative terms from the absolute value.

$3 | x |$