Simplify 5/(2 square root of 3)- square root of 3

$\frac{5}{2 \sqrt{3}} - \sqrt{3}$

Step 1

Simplify each term.

Multiply $\frac{5}{2 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{5}{2 \sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} - \sqrt{3}$

Combine and simplify the denominator.

Multiply $\frac{5}{2 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{5 \sqrt{3}}{2 \sqrt{3} \sqrt{3}} - \sqrt{3}$

Move $\sqrt{3}$ .

$\frac{5 \sqrt{3}}{2 (\sqrt{3} \sqrt{3})} - \sqrt{3}$

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

$\frac{5 \sqrt{3}}{2 ({\sqrt{3}}^{1} \sqrt{3})} - \sqrt{3}$

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

$\frac{5 \sqrt{3}}{2 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})} - \sqrt{3}$

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

$\frac{5 \sqrt{3}}{2 {\sqrt{3}}^{1 + 1}} - \sqrt{3}$

Add $1$ and $1$ .

$\frac{5 \sqrt{3}}{2 {\sqrt{3}}^{2}} - \sqrt{3}$

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

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

$\frac{5 \sqrt{3}}{2 {(3^{\frac{1}{2}})}^{2}} - \sqrt{3}$

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

$\frac{5 \sqrt{3}}{2 \cdot 3^{\frac{1}{2} \cdot 2}} - \sqrt{3}$

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

$\frac{5 \sqrt{3}}{2 \cdot 3^{\frac{2}{2}}} - \sqrt{3}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5 \sqrt{3}}{2 \cdot 3^{\frac{2}{2}}} - \sqrt{3}$

Rewrite the expression.

$\frac{5 \sqrt{3}}{2 \cdot 3^{1}} - \sqrt{3}$

Evaluate the exponent.

$\frac{5 \sqrt{3}}{2 \cdot 3} - \sqrt{3}$

Multiply $2$ by $3$ .

$\frac{5 \sqrt{3}}{6} - \sqrt{3}$

Step 2

To write $- \sqrt{3}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{5 \sqrt{3}}{6} - \sqrt{3} \cdot \frac{6}{6}$

Step 3

Combine fractions.

Combine $- \sqrt{3}$ and $\frac{6}{6}$ .

$\frac{5 \sqrt{3}}{6} + \frac{- \sqrt{3} \cdot 6}{6}$

Combine the numerators over the common denominator.

$\frac{5 \sqrt{3} - \sqrt{3} \cdot 6}{6}$

Step 4

Simplify the numerator.

Multiply $6$ by $- 1$ .

$\frac{5 \sqrt{3} - 6 \sqrt{3}}{6}$

Subtract $6 \sqrt{3}$ from $5 \sqrt{3}$ .

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

Step 5

Move the negative in front of the fraction.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 0.28867513 \dots$

Simplify 5/(2 square root of 3)- square root of 3

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