The problem asks us to find the length of the third side (hypotenuse) of a right triangle with two sides of length 3. 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 with two sides of length

3. The answer should be in simplest radical form.

2. Solution Steps

We can use the Pythagorean theorem to find the length of the hypotenuse. The Pythagorean theorem states that for a right triangle with sides $a$ and $b$ and hypotenuse $c$, we have $a^2 + b^2 = c^2$.

In this case, $a = 3$ and $b = 3$. Therefore, we have

$3^2 + 3^2 = c^2$

$9 + 9 = c^2$

$18 = c^2$

$c = \sqrt{18}$

Now we simplify the radical.

$\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}$

3. Final Answer

$3\sqrt{2}$