Simplify the Radical Expression (6 fourth root of 336)/(2 fourth root of 7)

$\frac{6 \sqrt[4]{336}}{2 \sqrt[4]{7}}$

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $6 \sqrt[4]{336}$ .

$\frac{2 (3 \sqrt[4]{336})}{2 \sqrt[4]{7}}$

Cancel the common factors.

Factor $2$ out of $2 \sqrt[4]{7}$ .

$\frac{2 (3 \sqrt[4]{336})}{2 (\sqrt[4]{7})}$

Cancel the common factor.

$\frac{2 (3 \sqrt[4]{336})}{2 \sqrt[4]{7}}$

Rewrite the expression.

$\frac{3 \sqrt[4]{336}}{\sqrt[4]{7}}$

Combine $\sqrt[4]{336}$ and $\sqrt[4]{7}$ into a single radical.

$3 \sqrt[4]{\frac{336}{7}}$

Divide $336$ by $7$ .

$3 \sqrt[4]{48}$

Rewrite $48$ as $2^{4} \cdot 3$ .

Factor $16$ out of $48$ .

$3 \sqrt[4]{16 (3)}$

Rewrite $16$ as $2^{4}$ .

$3 \sqrt[4]{2^{4} \cdot 3}$

Pull terms out from under the radical.

$3 (| 2 | \sqrt[4]{3})$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$3 (2 \sqrt[4]{3})$

Multiply $2$ by $3$ .

$6 \sqrt[4]{3}$

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt[4]{3}$

Decimal Form:

$7.89644407 \dots$