For example, the third root (also called the cube root) of 64 is 4, because if you multiply three fours together you get 64:

• The second root is usually called the "square root".
• The third root of a number is usually called the "cube root",
• After that, they are called the nth root, for example the 5th root, 7th root etc

Sometimes there are two roots

For every even-degree root (for example the 2nd, 4th, 6th ....) there are two roots. This is because multiplying two positive or two negative numbers both produce a positive result. For example, consider the square root of 9.

What number, multiplied by itself will produce 9?
Obviously 3 will work:

So to be precise, we say the "square root of 9 is plus and minus 3". This is written: The symbol in front of the 3 is read as "plus or minus".

This is true for every even order root, for example the 2nd, 4th, 6th and so on.

Sometimes there are no roots

When the root is of even degree ( for example the 2nd, 4th, 6th ....) you cannot find the root of a negative number. This is because there is no number, multiplied by itself, that produces a negative result*. For example, if you tried to find the square root of -9, you cannot do it. Both +3 and -3 would produce +9 when multiplied together.

With odd-degree roots such as the 3rd, fifth etc, you can find the root of a negative number and the root will have the same sign as the radicand. For example the cube root of -27 is -3, because

The symbols

Degree	The number of times the radicand is multiplied by itself. 2 means square root, 3 means cube root. After that they are called the 4th root, 5th root and so on. If this is missing, it is assumed to be 2 - the square root.
Radical symbol	The √ symbol that means "root of". The length of the horizontal bar is important. See note below.
Radicand	The thing you are finding the root of.

Another way to write it

Roots can also be written in exponent form. In general So for example the cube root of x would be written Which would be pronounced "x to the power of one third".