Finite Math Examples

$(\sqrt{5}, 0)$ , $(0, 2)$

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.

$\sqrt{{(0 - \sqrt{5})}^{2} + {(2 - 0)}^{2}}$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Simplify the expression.

Tap for more steps...

Step 3.1.1

Subtract $\sqrt{5}$ from $0$ .

$\sqrt{{(- \sqrt{5})}^{2} + {(2 - 0)}^{2}}$

Step 3.1.2

Apply the product rule to $- \sqrt{5}$ .

$\sqrt{{(- 1)}^{2} {\sqrt{5}}^{2} + {(2 - 0)}^{2}}$

Step 3.1.3

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

$\sqrt{1 {\sqrt{5}}^{2} + {(2 - 0)}^{2}}$

Step 3.1.4

Multiply ${\sqrt{5}}^{2}$ by $1$ .

$\sqrt{{\sqrt{5}}^{2} + {(2 - 0)}^{2}}$

Step 3.2

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

Tap for more steps...

Step 3.2.1

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

$\sqrt{{(5^{\frac{1}{2}})}^{2} + {(2 - 0)}^{2}}$

Step 3.2.2

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

$\sqrt{5^{\frac{1}{2} \cdot 2} + {(2 - 0)}^{2}}$

Step 3.2.3

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

$\sqrt{5^{\frac{2}{2}} + {(2 - 0)}^{2}}$

Step 3.2.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.4.1

Cancel the common factor.

$\sqrt{5^{\frac{2}{2}} + {(2 - 0)}^{2}}$

Step 3.2.4.2

Rewrite the expression.

$\sqrt{5^{1} + {(2 - 0)}^{2}}$

Step 3.2.5

Evaluate the exponent.

$\sqrt{5 + {(2 - 0)}^{2}}$

Step 3.3

Simplify the expression.

Tap for more steps...

Step 3.3.1

Subtract $0$ from $2$ .

$\sqrt{5 + 2^{2}}$

Step 3.3.2

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

$\sqrt{5 + 4}$

Step 3.3.3

Add $5$ and $4$ .

$\sqrt{9}$

Step 3.3.4

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

$\sqrt{3^{2}}$

Step 3.4

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

$3$

Step 4