Divide (3 square root of 8)/(4 square root of 6)

$\frac{3 \sqrt{8}}{4 \sqrt{6}}$

Combine $\sqrt{8}$ and $\sqrt{6}$ into a single radical.

$\frac{3 \sqrt{\frac{8}{6}}}{4}$

Cancel the common factor of $8$ and $6$ .

Factor $2$ out of $8$ .

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

Cancel the common factors.

Factor $2$ out of $6$ .

$\frac{3 \sqrt{\frac{2 \cdot 4}{2 \cdot 3}}}{4}$

Cancel the common factor.

$\frac{3 \sqrt{\frac{2 \cdot 4}{2 \cdot 3}}}{4}$

Rewrite the expression.

$\frac{3 \sqrt{\frac{4}{3}}}{4}$

Simplify the numerator.

Rewrite $\sqrt{\frac{4}{3}}$ as $\frac{\sqrt{4}}{\sqrt{3}}$ .

$\frac{3 \frac{\sqrt{4}}{\sqrt{3}}}{4}$

Simplify the numerator.

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

$\frac{3 \frac{\sqrt{2^{2}}}{\sqrt{3}}}{4}$

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

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

Multiply $\frac{2}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Combine and simplify the denominator.

Multiply $\frac{2}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{3 \frac{2 \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}}{4}$

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{3 \frac{2 \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}}{4}$

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

$\frac{3 \frac{2 \sqrt{3}}{{\sqrt{3}}^{1 + 1}}}{4}$

Add $1$ and $1$ .

$\frac{3 \frac{2 \sqrt{3}}{{\sqrt{3}}^{2}}}{4}$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{3 \frac{2 \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}}{4}$

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

$\frac{3 \frac{2 \sqrt{3}}{3^{\frac{1}{2} \cdot 2}}}{4}$

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

$\frac{3 \frac{2 \sqrt{3}}{3^{\frac{2}{2}}}}{4}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 \frac{2 \sqrt{3}}{3^{\frac{2}{2}}}}{4}$

Rewrite the expression.

$\frac{3 \frac{2 \sqrt{3}}{3^{1}}}{4}$

Evaluate the exponent.

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

Combine $3$ and $\frac{2 \sqrt{3}}{3}$ .

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

Multiply $3$ by $2$ .

$\frac{\frac{6 \sqrt{3}}{3}}{4}$

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{6 \sqrt{3}}{3}$ by cancelling the common factors.

Factor $3$ out of $6 \sqrt{3}$ .

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

Factor $3$ out of $3$ .

$\frac{\frac{3 (2 \sqrt{3})}{3 (1)}}{4}$

Cancel the common factor.

$\frac{\frac{3 (2 \sqrt{3})}{3 \cdot 1}}{4}$

Rewrite the expression.

$\frac{\frac{2 \sqrt{3}}{1}}{4}$

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

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

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 \sqrt{3}$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.86602540 \dots$

Divide (3 square root of 8)/(4 square root of 6)

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