2) Any value of x that makes 25 - 2x ≥ 0 but NOT a perfect square will mean that a radical will still remain in the expression......and the remaining radical WILL NOT be a rational number....to see this
Let x = 2 and we have that
√[25 - (2)(2) ] / 2 = √21 / 2 and √21/2 is NOT RATIONAL
So......we only get a rational whenever x = 8 or x = 12 thusly
√[25 - 2(8) ] / 2 = √9 / 2 = 3/2 which IS rational
And
√ [25 - 2(12) ] / 2 = √1 /2 = 1/2 which is also rational
So...remember.....any positive integer under the radical that is not a perfect square will produce an irrational
Hope that helps !!!
