Question

use the pythagorean theorem to find the distance between points p and q.
complete the equation to find c, the length of segment pq.
(type whole numbers.)
$c^2=(2)^2+(4)^2$
$c^2 = 4 + 16$
$c = \sqrt{20}$
the distance between point p and point q is \boxed{} unit(s).
(round to the nearest tenth as needed.)

Explanation:

Step1: Calculate the square root of 20

We know that \( c = \sqrt{20} \). First, we simplify \( \sqrt{20} \). We can factor 20 as \( 4\times5 \), so \( \sqrt{20}=\sqrt{4\times5}=\sqrt{4}\times\sqrt{5}=2\sqrt{5} \).

Step2: Approximate the value

Now, we approximate \( 2\sqrt{5} \). Since \( \sqrt{5}\approx2.236 \), then \( 2\times2.236 = 4.472 \). Rounding to the nearest tenth, we look at the hundredth place, which is 7. Since 7 > 5, we round up the tenth place. So \( 4.472\approx4.5 \).

Answer:

4.5