Question

find the distance between the two points in simplest radical form.

Explanation:

Step1: Identify the two points

The points are $(5, 5)$ and $(8, 1)$.

Step2: Apply distance formula

The distance formula is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. Substitute $x_1=5,y_1=5,x_2=8,y_2=1$:
$d=\sqrt{(8-5)^2+(1-5)^2}$

Step3: Calculate differences squared

Compute the terms inside the square root:
$d=\sqrt{(3)^2+(-4)^2}=\sqrt{9+16}$

Step4: Simplify the radical

Add and simplify the square root:
$d=\sqrt{25}=5$

Answer:

$5$