Simplify (8 square root of 24)/(2 square root of 48)

$\frac{8 \sqrt{24}}{2 \sqrt{48}}$

Cancel the common factor of $8$ and $2$ .

Factor $2$ out of $8 \sqrt{24}$ .

$\frac{2 (4 \sqrt{24})}{2 \sqrt{48}}$

Cancel the common factors.

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

$\frac{2 (4 \sqrt{24})}{2 (\sqrt{48})}$

Cancel the common factor.

$\frac{2 (4 \sqrt{24})}{2 \sqrt{48}}$

Rewrite the expression.

$\frac{4 \sqrt{24}}{\sqrt{48}}$

Combine $\sqrt{24}$ and $\sqrt{48}$ into a single radical.

$4 \sqrt{\frac{24}{48}}$

Cancel the common factor of $24$ and $48$ .

Factor $24$ out of $24$ .

$4 \sqrt{\frac{24 (1)}{48}}$

Cancel the common factors.

Factor $24$ out of $48$ .

$4 \sqrt{\frac{24 \cdot 1}{24 \cdot 2}}$

Cancel the common factor.

$4 \sqrt{\frac{24 \cdot 1}{24 \cdot 2}}$

Rewrite the expression.

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

Rewrite $\sqrt{\frac{1}{2}}$ as $\frac{\sqrt{1}}{\sqrt{2}}$ .

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

Any root of $1$ is $1$ .

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

Multiply $\frac{1}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Raise $\sqrt{2}$ to the power of $1$ .

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

Raise $\sqrt{2}$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

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

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$4 \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$2 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{2}$

Decimal Form:

$2.82842712 \dots$

Simplify (8 square root of 24)/(2 square root of 48)

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