To find the third side in simplest radical form of a right triangle given two sides, you can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, you have the square root of 93 as one of the sides (√93) and the other side is 2. Let's denote the third side as x.
So, according to the Pythagorean Theorem:
(√93)^2 + 2^2 = x^2
93 + 4 = x^2
97 = x^2
To simplify the radical form of x, we need to express 97 as a product of a perfect square and another number. Since 97 is a prime number, we cannot simplify it further.
Therefore, the third side in simplest radical form of the right triangle is √97.
