Find the Distance Between Two Points (2,2) , (5,5)

$(2, 2)$ , $(5, 5)$

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.

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

Step 3

Simplify.

Subtract $2$ from $5$ .

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

Raise $3$ to the power of $2$ .

$\sqrt{9 + {(5 - 2)}^{2}}$

Subtract $2$ from $5$ .

$\sqrt{9 + 3^{2}}$

Raise $3$ to the power of $2$ .

$\sqrt{9 + 9}$

Add $9$ and $9$ .

$\sqrt{18}$

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$\sqrt{9 (2)}$

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

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

Pull terms out from under the radical.

$3 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{2}$

Decimal Form:

$4.24264068 \dots$

Step 5