Answer: 2. x = √3 3. y = 3√2 4. a = (2/3)√2Step-by-step explanation:In an isosceles right triangle, the length of the hypotenuse is √2 times the length of one side. Said another way, the length of the side is 1/√2 times the length of the hypotenuse.___2. x = √6/√2 = √(6/2) = √3 . . . . . divide the hypotenuse by √2 to find x___3. (12 -√2y) = √2y . . . . . equate the hypotenuse to √2 times the leg and solve 12 = 2√2y 12/(2√2) = y = 6/√2 = 3√2___4. 3a = 2√2 . . . . . . equate the hypotenuse to √2 times the leg and solve a = 2√2/3 = (2/3)√2_____Comment on "rationalizing the denominator""Simplest radical form" usually means the radical is in the numerator. To eliminate it from the denominator, multiply by the radical: 1/√n = (√n)/(√n) · 1/√n = (√n)/(√n)^2 = (√n)/nThat is, ... 1/√2 = (√2)/2 . . . . for example.