**Quote:**

So if both conditions are true then we can conclude that √(56*x*) is not an integer, correct?

No. For example these two values fit the both statements:

*x* = 14

(1) x =

14 is a multiple of 14

(2) 28 is not a factor of x =

14and

*x* = 42

(1) x =

42 is a multiple of 14

(2) 28 is not a factor of x =

42And these two values yield different answers to the main question "Is √(56

*x*) an integer?"

IF

*x* = 14, then √(56

*x*) = 28 . It is an integer!

*√(56 × 14) = √(14 × 4 × 14) = 14 × 2 = 28*IF

*x* = 42, then √(56

*x*) = 28√3 . It is NOT an integer!

*√(56 × 42) = √(14 × 4 × 14 × 3) = 14 × 2 × √3 = 28√3*So the both statements combined are NOT sufficient to give a definite answer to the main question.