Question

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

Explanation:

Step1: Identify the two points

The points are $(-8, -9)$ and $(-3, -5)$.

Step2: Apply distance formula

The distance formula is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
Substitute $x_1=-8, y_1=-9, x_2=-3, y_2=-5$:
$d=\sqrt{(-3-(-8))^2+(-5-(-9))^2}$

Step3: Simplify inside the square root

Calculate differences:
$(-3-(-8))=5$, $(-5-(-9))=4$
$d=\sqrt{5^2+4^2}=\sqrt{25+16}$

Step4: Compute final radical form

$d=\sqrt{41}$

Answer:

$\sqrt{41}$