In the Real Numbers, you follow something like this stream of logic.

Right-Hand Side

x^4 is positive

8 is positive

1 is positive

Negative sign - The right hand side is negative. It cannot be positive. It cannot be zero.

Left-Hand Side

y^2 is positive

How many positive numbers can you name that are equal to a negative number?

Note: When did 2 get to be the square root of 8? Cube root, perhaps.