The value of square root of x is between 84/18 and the square root of 41 . Why are there only two possible values of x?

Answer 1

I assume that x is a whole number. I start with what I'm given in the problem: 84/18 < sqrt(x) < sqrt(41). Most people would rather not deal with square roots, so I eliminate them by squaring. However, to make sure the inequality stays true, I must square all three numbers, not just sqrt(x) and sqrt(41). (84/18)^2=4.7, and squaring each of the other numbers cancels out the square root. (Squaring and taking the square root are opposites.) So I have 4.7 < x < 6.4. There are only two whole numbers between 4.7 and 6.4. x must be 5 or 6.