Simplify square root of (2160x^8)/(60x^2)

$\sqrt{\frac{2160 x^{8}}{60 x^{2}}}$

Step 1

Reduce the expression $\frac{2160 x^{8}}{60 x^{2}}$ by cancelling the common factors.

Factor $60$ out of $2160 x^{8}$ .

$\sqrt{\frac{60 (36 x^{8})}{60 x^{2}}}$

Factor $60$ out of $60 x^{2}$ .

$\sqrt{\frac{60 (36 x^{8})}{60 (x^{2})}}$

Cancel the common factor.

$\sqrt{\frac{60 (36 x^{8})}{60 x^{2}}}$

Rewrite the expression.

$\sqrt{\frac{36 x^{8}}{x^{2}}}$

Step 2

Cancel the common factor of $x^{8}$ and $x^{2}$ .

Factor $x^{2}$ out of $36 x^{8}$ .

$\sqrt{\frac{x^{2} (36 x^{6})}{x^{2}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt{\frac{x^{2} (36 x^{6})}{x^{2} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x^{2} (36 x^{6})}{x^{2} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{36 x^{6}}{1}}$

Divide $36 x^{6}$ by $1$ .

$\sqrt{36 x^{6}}$

Step 3

Rewrite $36 x^{6}$ as ${(6 x^{3})}^{2}$ .

$\sqrt{{(6 x^{3})}^{2}}$

Step 4

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

$6 x^{3}$