Y = sqrt(x)^2, can x be negative?

Question

Basically, does the sqauring cancel out the square root, or does the "no negative square roots" rule still aply?

Answer 1

y = √(x²) <- This expression can have x negative
y = (√x)² <- This expression can not have x negative

Answer 2

Of course x can be negative, that is why there are imaginary numbers. Methinks you REALLY want to know if
x = (sqrt(x))^2

If you have learned imaginary numbers, the answer is YES. Imaginary numbers exist to allow us to take the square root of negative numbers.

If you have not learned imaginary numbers, the answer is YES, as long as x is greater than or equal to zero. Because if x is less than zero there is no solution because you cannot take the square root of a negative number.

Answer 3

the square root of x^2 is just x
therefore y=x
you can't do a square root of a negative number, so no it can't be negative

Answer 4

x, negative or not, Y remains the same, +-x. I'm not sure if you're squaring x or sqrt(x).

For example take x=-9 then sqrt(-9) = +-3i

(+-3i)^2 = -+9 both are solutions