What Does This Symbol Mean?

The symbol you show designates the "square root of x". The square root of a number or expression is a value such that when it is multiplied by itself, the result is whatever it was you took the square root of.

Example
√(16) = 4, because 4*4 = 16.
√(16) = -4, because -4*-4 = 16.

As suggested by the above, any positive real number has two square roots. 16 has square roots +4 and -4.

Similarly,
√(x²) = ±x, because x*x = x², and (-x)(-x) = x².

Another way to show the square root is with a fractional power: X^1/2. If you multiply this by itself, the result is x. (x^1/2)(x^1/2) = x^(1/2)+(1/2) = x^2/2 = x¹ = x
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If the radical symbol has a number other than "nothing" or 2 in the "notch", that designates a root other than the square root. The n^th root must be taken to the n^th power to get back to the original value. The 3^rd, or cube, root of 27 is 3, which means that 3*3*3 = 3³ = 27. We can also write this 27^1/3 = 3.

The picture shows a symbol used for the square root of x.

Example, √16 = 4

Some computer symbols such as √ can't do the overbar on top of the x.  In that case, you would need parenthesis to indicate the contents of the square root symbol if they are ambiguous.

The picture refers to surds.  A surd is the square root of a number that isn't a square number for example if the number was /50 we would do /5 x /10 and then that then equals 5/2 by the way / means square root.  It does get much harder than this but this should get you through homework

That symbol [without the X] is called RADICAL. Radical can refer to many different things and concept. Here, en.wikipedia.org  try this website.

i just learned that today from my teacher. But I'm not sure though. I hope I'm right.

It means x divided by something

The square root of x it is a very common calculus symbol

That symbol simple means the squareroot of a number x.