Question

1. use pythagorean theorem to find the value of x. if possible, simplify the square root.

Explanation:

Step1: Recall Pythagorean Theorem

For right triangle: $a^2 + b^2 = c^2$, where $c$ is hypotenuse. Here, $x$ is hypotenuse, so $5^2 + 20^2 = x^2$.

Step2: Calculate squared side values

$5^2 = 25$, $20^2 = 400$
$25 + 400 = x^2$

Step3: Sum and solve for x

$425 = x^2$
$x = \sqrt{425} = \sqrt{25 \times 17} = 5\sqrt{17}$

Answer:

$5\sqrt{17}$