Evaluate 0.5/(( square root of 3)/2)

$\frac{0.5}{\frac{\sqrt{3}}{2}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$0.5 \frac{2}{\sqrt{3}}$

Step 2

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

$0.5 (\frac{2}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}})$

Step 3

Combine and simplify the denominator.

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

$0.5 \frac{2 \sqrt{3}}{\sqrt{3} \sqrt{3}}$

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

$0.5 \frac{2 \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

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

$0.5 \frac{2 \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

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

$0.5 \frac{2 \sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Add $1$ and $1$ .

$0.5 \frac{2 \sqrt{3}}{{\sqrt{3}}^{2}}$

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

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

$0.5 \frac{2 \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}$

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

$0.5 \frac{2 \sqrt{3}}{3^{\frac{1}{2} \cdot 2}}$

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

$0.5 \frac{2 \sqrt{3}}{3^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$0.5 \frac{2 \sqrt{3}}{3^{\frac{2}{2}}}$

Rewrite the expression.

$0.5 \frac{2 \sqrt{3}}{3^{1}}$

Evaluate the exponent.

$0.5 \frac{2 \sqrt{3}}{3}$

Step 4

Cancel the common factor of $0.5$ .

Factor $0.5$ out of $3$ .

$0.5 \frac{2 \sqrt{3}}{0.5 (6)}$

Cancel the common factor.

$0.5 \frac{2 \sqrt{3}}{0.5 \cdot 6}$

Rewrite the expression.

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

Step 5

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

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

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

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.57735026 \dots$

Evaluate 0.5/(( square root of 3)/2)

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