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

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

Step 1

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

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

Step 2

Combine and simplify the denominator.

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Step 3

Apply the distributive property.

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

Step 4

Multiply $- \sqrt{3} \sqrt{3}$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

Step 5

Simplify each term.

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{3 \sqrt{3} - 3^{1}}{3}$

Evaluate the exponent.

$\frac{3 \sqrt{3} - 1 \cdot 3}{3}$

Multiply $- 1$ by $3$ .

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

Step 6

Cancel the common factor of $3 \sqrt{3} - 3$ and $3$ .

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

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

Factor $3$ out of $- 3$ .

$\frac{3 (\sqrt{3}) + 3 \cdot - 1}{3}$

Factor $3$ out of $3 (\sqrt{3}) + 3 (- 1)$ .

$\frac{3 (\sqrt{3} - 1)}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{3 (\sqrt{3} - 1)}{3 (1)}$

Cancel the common factor.

$\frac{3 (\sqrt{3} - 1)}{3 \cdot 1}$

Rewrite the expression.

$\frac{\sqrt{3} - 1}{1}$

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

$\sqrt{3} - 1$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3} - 1$

Decimal Form:

$0.73205080 \dots$

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

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