The problem asks us to find the length of the third side (hypotenuse) of a right triangle, given the lengths of the other two sides (legs), which are 2 and 5. The answer should be in simplest radical form.

1. Problem Description

The problem asks us to find the length of the third side (hypotenuse) of a right triangle, given the lengths of the other two sides (legs), which are 2 and

5. The answer should be in simplest radical form.

2. Solution Steps

We can use the Pythagorean theorem to find the length of the hypotenuse, denoted by $c$. The Pythagorean theorem states that in a right triangle with legs of length $a$ and $b$, and hypotenuse of length $c$, we have

$a^2 + b^2 = c^2$.

In this case, $a=2$ and $b=5$, so we have

$2^2 + 5^2 = c^2$

$4 + 25 = c^2$

$29 = c^2$

Taking the square root of both sides, we get

$c = \sqrt{29}$

Since 29 is a prime number, we cannot simplify the square root further.

3. Final Answer

$\sqrt{29}$