Basic Math Examples

$(0, 0)$ , $(- \frac{1}{2}, \frac{1}{9})$

Step 1

Use the distance formula to determine the distance between the two points.

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Step 2

Substitute the actual values of the points into the distance formula.

$\sqrt{{((- \frac{1}{2}) - 0)}^{2} + {(\frac{1}{9} - 0)}^{2}}$

Step 3

Simplify.

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Step 3.1

Subtract $0$ from $- \frac{1}{2}$ .

$\sqrt{{(- \frac{1}{2})}^{2} + {(\frac{1}{9} - 0)}^{2}}$

Step 3.2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.2.1

Apply the product rule to $- \frac{1}{2}$ .

$\sqrt{{(- 1)}^{2} {(\frac{1}{2})}^{2} + {(\frac{1}{9} - 0)}^{2}}$

Step 3.2.2

Apply the product rule to $\frac{1}{2}$ .

$\sqrt{{(- 1)}^{2} \frac{1^{2}}{2^{2}} + {(\frac{1}{9} - 0)}^{2}}$

Step 3.3

Raise $- 1$ to the power of $2$ .

$\sqrt{1 \frac{1^{2}}{2^{2}} + {(\frac{1}{9} - 0)}^{2}}$

Step 3.4

Multiply $\frac{1^{2}}{2^{2}}$ by $1$ .

$\sqrt{\frac{1^{2}}{2^{2}} + {(\frac{1}{9} - 0)}^{2}}$

Step 3.5

One to any power is one.

$\sqrt{\frac{1}{2^{2}} + {(\frac{1}{9} - 0)}^{2}}$

Step 3.6

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

$\sqrt{\frac{1}{4} + {(\frac{1}{9} - 0)}^{2}}$

Step 3.7

Subtract $0$ from $\frac{1}{9}$ .

$\sqrt{\frac{1}{4} + {(\frac{1}{9})}^{2}}$

Step 3.8

Apply the product rule to $\frac{1}{9}$ .

$\sqrt{\frac{1}{4} + \frac{1^{2}}{9^{2}}}$

Step 3.9

One to any power is one.

$\sqrt{\frac{1}{4} + \frac{1}{9^{2}}}$

Step 3.10

Raise $9$ to the power of $2$ .

$\sqrt{\frac{1}{4} + \frac{1}{81}}$

Step 3.11

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{81}{81}$ .

$\sqrt{\frac{1}{4} \cdot \frac{81}{81} + \frac{1}{81}}$

Step 3.12

To write $\frac{1}{81}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\sqrt{\frac{1}{4} \cdot \frac{81}{81} + \frac{1}{81} \cdot \frac{4}{4}}$

Step 3.13

Write each expression with a common denominator of $324$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.13.1

Multiply $\frac{1}{4}$ by $\frac{81}{81}$ .

$\sqrt{\frac{81}{4 \cdot 81} + \frac{1}{81} \cdot \frac{4}{4}}$

Step 3.13.2

Multiply $4$ by $81$ .

$\sqrt{\frac{81}{324} + \frac{1}{81} \cdot \frac{4}{4}}$

Step 3.13.3

Multiply $\frac{1}{81}$ by $\frac{4}{4}$ .

$\sqrt{\frac{81}{324} + \frac{4}{81 \cdot 4}}$

Step 3.13.4

Multiply $81$ by $4$ .

$\sqrt{\frac{81}{324} + \frac{4}{324}}$

Step 3.14

Combine the numerators over the common denominator.

$\sqrt{\frac{81 + 4}{324}}$

Step 3.15

Add $81$ and $4$ .

$\sqrt{\frac{85}{324}}$

Step 3.16

Rewrite $\sqrt{\frac{85}{324}}$ as $\frac{\sqrt{85}}{\sqrt{324}}$ .

$\frac{\sqrt{85}}{\sqrt{324}}$

Step 3.17

Simplify the denominator.

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Step 3.17.1

Rewrite $324$ as $18^{2}$ .

$\frac{\sqrt{85}}{\sqrt{18^{2}}}$

Step 3.17.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{\sqrt{85}}{18}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{85}}{18}$

Decimal Form:

$0.51219691 \dots$

Step 5