Simplify (6 square root of 48)/(4 square root of 6)

$\frac{6 \sqrt{48}}{4 \sqrt{6}}$

Cancel the common factor of $6$ and $4$ .

Factor $2$ out of $6 \sqrt{48}$ .

$\frac{2 (3 \sqrt{48})}{4 \sqrt{6}}$

Cancel the common factors.

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

$\frac{2 (3 \sqrt{48})}{2 (2 \sqrt{6})}$

Cancel the common factor.

$\frac{2 (3 \sqrt{48})}{2 (2 \sqrt{6})}$

Rewrite the expression.

$\frac{3 \sqrt{48}}{2 \sqrt{6}}$

$\frac{3 \sqrt{48}}{2 \sqrt{6}}$

$\frac{3 \sqrt{48}}{2 \sqrt{6}}$

Combine $\sqrt{48}$ and $\sqrt{6}$ into a single radical.

$\frac{3 \sqrt{\frac{48}{6}}}{2}$

Cancel the common factor of $48$ and $6$ .

Factor $6$ out of $48$ .

$\frac{3 \sqrt{\frac{6 \cdot 8}{6}}}{2}$

Cancel the common factors.

Factor $6$ out of $6$ .

$\frac{3 \sqrt{\frac{6 \cdot 8}{6 (1)}}}{2}$

Cancel the common factor.

$\frac{3 \sqrt{\frac{6 \cdot 8}{6 \cdot 1}}}{2}$

Rewrite the expression.

$\frac{3 \sqrt{\frac{8}{1}}}{2}$

Divide $8$ by $1$ .

$\frac{3 \sqrt{8}}{2}$

$\frac{3 \sqrt{8}}{2}$

$\frac{3 \sqrt{8}}{2}$

Simplify the numerator.

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$\frac{3 \sqrt{4 (2)}}{2}$

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

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

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

Pull terms out from under the radical.

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

Multiply $3$ by $2$ .

$\frac{6 \sqrt{2}}{2}$

$\frac{6 \sqrt{2}}{2}$

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

Factor $2$ out of $6 \sqrt{2}$ .

$\frac{2 (3 \sqrt{2})}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 (3 \sqrt{2})}{2 (1)}$

Cancel the common factor.

$\frac{2 (3 \sqrt{2})}{2 \cdot 1}$

Rewrite the expression.

$\frac{3 \sqrt{2}}{1}$

Divide $3 \sqrt{2}$ by $1$ .

$3 \sqrt{2}$

$3 \sqrt{2}$

$3 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{2}$

Decimal Form:

$4.24264068 \dots$

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