Question

find the value of x. if necessary, write your answer in simplest radical form.
$x=\square$
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, $a^2 + b^2 = c^2$, where $c$ is the hypotenuse. Here, $a=3$, $b=4$, $c=x$.
$\implies 3^2 + 4^2 = x^2$

Step2: Calculate squared terms

Compute the squares of the legs.
$\implies 9 + 16 = x^2$

Step3: Sum and solve for x

Add the values, then take the square root.
$\implies 25 = x^2 \implies x = \sqrt{25} = 5$

Answer:

$5$