Algebra Examples

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

Step 1

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

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

Step 2

Combine and simplify the denominator.

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Step 2.1

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

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

Step 2.2

Move $\sqrt{5}$ .

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

Step 2.3

Raise $\sqrt{5}$ to the power of $1$ .

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

Step 2.4

Raise $\sqrt{5}$ to the power of $1$ .

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

Step 2.5

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

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

Step 2.6

Add $1$ and $1$ .

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

Step 2.7

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

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Step 2.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

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

Step 2.7.2

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

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

Step 2.7.3

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

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

Step 2.7.4

Cancel the common factor of $2$ .

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Step 2.7.4.1

Cancel the common factor.

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

Step 2.7.4.2

Rewrite the expression.

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

Step 2.7.5

Evaluate the exponent.

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

Step 3

Cancel the common factor of $5$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 1.11803398 \dots$