Question

find the distance between the two points in simplest radical form.
(7,1) and (4,5)

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 7$, $y_1 = 1$, $x_2 = 4$, and $y_2 = 5$.

Step2: Substitute values

$d=\sqrt{(4 - 7)^2+(5 - 1)^2}=\sqrt{(-3)^2+4^2}$.

Step3: Calculate squares

$\sqrt{(-3)^2+4^2}=\sqrt{9 + 16}$.

Step4: Add values inside square - root

$\sqrt{9+16}=\sqrt{25}$.

Step5: Simplify square - root

$\sqrt{25}=5$.

Answer:

$5$