Algebra Examples

\frac{9}{\sqrt{3}}

$\frac{9}{\sqrt{3}}$

Step 1

Multiply

\frac{9}{\sqrt{3}}

$\frac{9}{\sqrt{3}}$ by

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

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

\frac{9}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}

$\frac{9}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply

$\frac{9}{\sqrt{3}}$ by

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

$\frac{9 \sqrt{3}}{\sqrt{3} \sqrt{3}}$

Step 2.2

Raise

$\sqrt{3}$ to the power of

$1$ .

$\frac{9 \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

Step 2.3

Raise

$\sqrt{3}$ to the power of

$1$ .

$\frac{9 \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

Step 2.4

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{9 \sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Step 2.5

Add

$1$ and

$1$ .

$\frac{9 \sqrt{3}}{{\sqrt{3}}^{2}}$

Step 2.6

Rewrite

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

$3$ .

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Step 2.6.1

Use

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

$\sqrt{3}$ as

$3^{\frac{1}{2}}$ .

$\frac{9 \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}$

Step 2.6.2

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$\frac{9 \sqrt{3}}{3^{\frac{1}{2} \cdot 2}}$

Step 2.6.3

Combine

$\frac{1}{2}$ and

$2$ .

$\frac{9 \sqrt{3}}{3^{\frac{2}{2}}}$

Step 2.6.4

Cancel the common factor of

$2$ .

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Step 2.6.4.1

Cancel the common factor.

$\frac{9 \sqrt{3}}{3^{\frac{2}{2}}}$

Step 2.6.4.2

Rewrite the expression.

$\frac{9 \sqrt{3}}{3^{1}}$

$\frac{9 \sqrt{3}}{3^{1}}$

Step 2.6.5

Evaluate the exponent.

$\frac{9 \sqrt{3}}{3}$

$\frac{9 \sqrt{3}}{3}$

$\frac{9 \sqrt{3}}{3}$

Step 3

Cancel the common factor of

$9$ and

$3$ .

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Step 3.1

Factor

$3$ out of

$9 \sqrt{3}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor

$3$ out of

$3$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 3.2.4

Divide

$3 \sqrt{3}$ by

$1$ .

$3 \sqrt{3}$

$3 \sqrt{3}$

$3 \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{3}$

Decimal Form:

$5.19615242 \dots$

$\frac{9}{\sqrt[]{3}}$

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