Simplify (8 square root of 24)/(16 square root of 6)

$\frac{8 \sqrt{24}}{16 \sqrt{6}}$

Step 1

Cancel the common factor of $8$ and $16$ .

Factor $8$ out of $8 \sqrt{24}$ .

$\frac{8 (\sqrt{24})}{16 \sqrt{6}}$

Cancel the common factors.

Factor $8$ out of $16 \sqrt{6}$ .

$\frac{8 (\sqrt{24})}{8 (2 \sqrt{6})}$

Cancel the common factor.

$\frac{8 \sqrt{24}}{8 (2 \sqrt{6})}$

Rewrite the expression.

$\frac{\sqrt{24}}{2 \sqrt{6}}$

Step 2

Combine $\sqrt{24}$ and $\sqrt{6}$ into a single radical.

$\frac{\sqrt{\frac{24}{6}}}{2}$

Step 3

Cancel the common factor of $24$ and $6$ .

Factor $6$ out of $24$ .

$\frac{\sqrt{\frac{6 \cdot 4}{6}}}{2}$

Cancel the common factors.

Factor $6$ out of $6$ .

$\frac{\sqrt{\frac{6 \cdot 4}{6 (1)}}}{2}$

Cancel the common factor.

$\frac{\sqrt{\frac{6 \cdot 4}{6 \cdot 1}}}{2}$

Rewrite the expression.

$\frac{\sqrt{\frac{4}{1}}}{2}$

Divide $4$ by $1$ .

$\frac{\sqrt{4}}{2}$

Step 4

Simplify the numerator.

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

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

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

$\frac{2}{2}$

Step 5

Divide $2$ by $2$ .

$1$