What is the value of x?

x = 3 sqrt 2

Step-by-step explanation:

We know that this is a 45, 45m 90 special right triangle. In this special right triangle the side lengths are x, x and the hypotenuse is x sqrt 2 (we can prove this using pythagoreans theorem). 6 is the hypotenuse, meaning that it is equal to x sqrt 2:

6 = x sqrt 2

x = 6/sqrt 2

Rationalize the denominator:

x = (6 sqrt 2)/2

x = 3 sqrt 2

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743