Basic Math Examples

$\frac{- 6}{\sqrt{20}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 1.1.1

Factor $4$ out of $20$ .

$\frac{- 6}{\sqrt{4 (5)}}$

Step 1.1.2

Rewrite $4$ as $2^{2}$ .

$\frac{- 6}{\sqrt{2^{2} \cdot 5}}$

Step 1.2

Pull terms out from under the radical.

$\frac{- 6}{2 \sqrt{5}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $- 6$ and $2$ .

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Step 2.1.1

Factor $2$ out of $- 6$ .

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

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $2$ out of $2 \sqrt{5}$ .

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

Step 2.1.2.2

Cancel the common factor.

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

Step 2.1.2.3

Rewrite the expression.

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

Step 2.2

Move the negative in front of the fraction.

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

Step 3

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

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

Step 4

Combine and simplify the denominator.

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

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

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

Step 4.5

Add $1$ and $1$ .

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

Step 4.6

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

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Step 4.6.1

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

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

Step 4.6.2

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

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

Step 4.6.3

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

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

Step 4.6.4

Cancel the common factor of $2$ .

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Step 4.6.4.1

Cancel the common factor.

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

Step 4.6.4.2

Rewrite the expression.

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

Step 4.6.5

Evaluate the exponent.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 1.34164078 \dots$