Simplify (2 square root of 2)/(8 square root of 3)

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

Step 1

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

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

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

Cancel the common factors.

Factor $2$ out of $8 \sqrt{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Multiply $\frac{\sqrt{2}}{4 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Step 3

Combine and simplify the denominator.

Multiply $\frac{\sqrt{2}}{4 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Move $\sqrt{3}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Step 4

Simplify the numerator.

Combine using the product rule for radicals.

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

Multiply $2$ by $3$ .

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

Step 5

Multiply $4$ by $3$ .

$\frac{\sqrt{6}}{12}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{6}}{12}$

Decimal Form:

$0.20412414 \dots$

Simplify (2 square root of 2)/(8 square root of 3)

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