Question

what is the value of x 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 $x$, $a=24$, $b=7$.
$$24^2 + 7^2 = x^2$$

Step2: Calculate squared terms

Compute the squares of the legs.
$$576 + 49 = x^2$$

Step3: Sum and solve for x

Add the values, then take the square root.
$$625 = x^2 \implies x = \sqrt{625} = 25$$

Answer:

25