Algebra Examples

$\frac{6}{\sqrt{9 - {(6)}^{2}}}$

Step 1

Simplify the denominator.

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Step 1.1

Raise $6$ to the power of $2$ .

$\frac{6}{\sqrt{9 - 1 \cdot 36}}$

Step 1.2

Multiply $- 1$ by $36$ .

$\frac{6}{\sqrt{9 - 36}}$

Step 1.3

Subtract $36$ from $9$ .

$\frac{6}{\sqrt{- 27}}$

Step 1.4

Rewrite $- 27$ as $- 1 (27)$ .

$\frac{6}{\sqrt{- 1 (27)}}$

Step 1.5

Rewrite $\sqrt{- 1 (27)}$ as $\sqrt{- 1} \cdot \sqrt{27}$ .

$\frac{6}{\sqrt{- 1} \cdot \sqrt{27}}$

Step 1.6

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{6}{i \cdot \sqrt{27}}$

Step 1.7

Rewrite $27$ as $3^{2} \cdot 3$ .

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Step 1.7.1

Factor $9$ out of $27$ .

$\frac{6}{i \cdot \sqrt{9 (3)}}$

Step 1.7.2

Rewrite $9$ as $3^{2}$ .

$\frac{6}{i \cdot \sqrt{3^{2} \cdot 3}}$

Step 1.8

Pull terms out from under the radical.

$\frac{6}{i \cdot (3 \sqrt{3})}$

Step 1.9

Move $3$ to the left of $i$ .

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

Step 2

Cancel the common factor of $6$ and $3$ .

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Step 2.1

Factor $3$ out of $6$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

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

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

Step 4

Combine and simplify the denominator.

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Step 4.1

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

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

Step 4.2

Move $\sqrt{3}$ .

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

Step 4.3

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

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

Step 4.4

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

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

Step 4.5

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

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

Step 4.6

Add $1$ and $1$ .

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

Step 4.7

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

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Step 4.7.1

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

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

Step 4.7.2

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

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

Step 4.7.3

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

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

Step 4.7.4

Cancel the common factor of $2$ .

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Step 4.7.4.1

Cancel the common factor.

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

Step 4.7.4.2

Rewrite the expression.

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

Step 4.7.5

Evaluate the exponent.

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

Step 5

Move $3$ to the left of $i$ .

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