Simplify ( square root of 60x^4)/( square root of 5x^4)

$\frac{\sqrt{60 x^{4}}}{\sqrt{5 x^{4}}}$

Combine $\sqrt{60 x^{4}}$ and $\sqrt{5 x^{4}}$ into a single radical.

$\sqrt{\frac{60 x^{4}}{5 x^{4}}}$

Reduce the expression $\frac{60 x^{4}}{5 x^{4}}$ by cancelling the common factors.

Factor $5$ out of $60 x^{4}$ .

$\sqrt{\frac{5 (12 x^{4})}{5 x^{4}}}$

Factor $5$ out of $5 x^{4}$ .

$\sqrt{\frac{5 (12 x^{4})}{5 (x^{4})}}$

Cancel the common factor.

$\sqrt{\frac{5 (12 x^{4})}{5 x^{4}}}$

Rewrite the expression.

$\sqrt{\frac{12 x^{4}}{x^{4}}}$

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

Cancel the common factor.

$\sqrt{\frac{12 x^{4}}{x^{4}}}$

Divide $12$ by $1$ .

$\sqrt{12}$

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$\sqrt{4 (3)}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 3}$

Pull terms out from under the radical.

$2 \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{3}$

Decimal Form:

$3.46410161 \dots$