must be true

[sanju09]

If x and y are real numbers and the square of y is equal to the square root of x, which of the following must be true?

I. x = y^4
II. x ≥ 0
III. y ≥ 0

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III

[truplayer256]

If x and y are real numbers and the square of y is equal to the square root of x, which of the following must be true?

I. x = y^4
II. x ≥ 0
III. y ≥ 0

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III

The answer's B. We're given that y^2=sqrt(x). We can automatically assume that option 2 is correct since we cannot have a number less than zero under a radical. For option 1, if we square both sides of the equation y^2=sqrt(x), we get y^4=x. Option 3 doesn't necessarily have to be true. Because let's say x=25^2, then y^2 has to equal 25. y^2=25 , y=plus or minus 5 and minus 5 doesn't fit y is greater than or equal to zero.

[sanju09]

The answer's B

readers want to know what is in your mind when you declare something as your answer, trueplayer!