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,

√(x

Another way to show the square root is with a fractional power: X

_____

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

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,

√(x

^{2}) = ±x, because x*x = x^{2}, and (-x)(-x) = x^{2}.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}= x^{1}= x_____

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 = 3^{3}= 27. We can also write this 27^{1/3}= 3.