Question

find the distance between the two points in simplest radical form.
(0, 3) and (6, 0)

Explanation:

Step1: Recall distance formula

The distance $d$ between points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step2: Substitute given points

Let $(x_1,y_1)=(0,3)$ and $(x_2,y_2)=(6,0)$. Substitute values:
$d=\sqrt{(6-0)^2+(0-3)^2}$

Step3: Simplify the expression

Calculate squared terms:
$d=\sqrt{6^2+(-3)^2}=\sqrt{36+9}=\sqrt{45}$

Step4: Simplify radical

Factor 45 into $9\times5$:
$d=\sqrt{9\times5}=\sqrt{9}\times\sqrt{5}=3\sqrt{5}$

Answer:

$3\sqrt{5}$