Simplify square root of (36x^8)/(4x^6)

$\sqrt{\frac{36 x^{8}}{4 x^{6}}}$

Step 1

Reduce the expression $\frac{36 x^{8}}{4 x^{6}}$ by cancelling the common factors.

Factor $4$ out of $36 x^{8}$ .

$\sqrt{\frac{4 (9 x^{8})}{4 x^{6}}}$

Factor $4$ out of $4 x^{6}$ .

$\sqrt{\frac{4 (9 x^{8})}{4 (x^{6})}}$

Cancel the common factor.

$\sqrt{\frac{4 (9 x^{8})}{4 x^{6}}}$

Rewrite the expression.

$\sqrt{\frac{9 x^{8}}{x^{6}}}$

Step 2

Cancel the common factor of $x^{8}$ and $x^{6}$ .

Factor $x^{6}$ out of $9 x^{8}$ .

$\sqrt{\frac{x^{6} (9 x^{2})}{x^{6}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt{\frac{x^{6} (9 x^{2})}{x^{6} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x^{6} (9 x^{2})}{x^{6} \cdot 1}}$

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, assuming positive real numbers.

$3 x$