A square has side length 95. The length of the diagonal of the square is? Express your answer in simplest radical form.

The correct answer is: 95√2

The side of the given square is 95.
We are asked to find the diagonal.
The properties of a square are as follows:
1) A square has all sides of equal length
2) A square has all angles 90°.
3) A diagonal joins the opposite corners of the square. It forms two right-angled triangles of the square.
Let the four corners of the square be ABCD
We will consider the sides AB and BC.
The diagonal will be AC.
The angle between the sides AB and BC is 90°. The diagonal will be the side opposite to this angle.
So, the diagonal is the hypotenuse of the triangle ABC formed due to the diagonal.
As it is a right-angled triangle, we will use the Pythagoras theorem.
Pythagoras theorem states that the square of the hypotenuse is equal to the sum of the square of the two sides.
AC² = AB² + BC²
= 95² + 95²
= 9025 + 9025
= 18050
Taking the square root of the both sides, we can write the equation as follows.
AC = 134.4
So, the value of the hypotenuse is 134.4

For such questions, we should know the properties of the right-angled triangle. The other method to solve it will be 45°-45°-90° theorem.  Due to diagonal, the triangle which is formed has the sides in proportion 1:1:√2. Therefore, the value of hypotenuse is given by √2 multiplied by the value of the side.