Chapters

Exact square root
Perfect Square
Not exact square root

The root is the inverse operation to the exponentiation. In other words, the square root is a factor of a number which will become the original number when multiplied by itself. For example, the square root of $4$ is $2$ but if $2$ is multiplied by itself, it will result in the original number (which is $4$ ). Another example is $49$ , the square root of $49$ is $7$ but if $7$ is multiplied by itself then it will result in the original number (which is $49$ ). Given two numbers, called the radicand and index, find a third number, which is called the root, such that when elevated to the index, it is equal to the radicand.

$\sqrt [ index ]{ Radicand } =Root$

The index for the square root is $2$ , although in this case it is omitted. Let's come back to all previous examples and describe them. In the first example, the number is $4$ and the index will be $2$ , radicant will be $4$ and the root will be $2$ . In the case of the second example, the number is $49$ and the index is the same (which is $2$ ). The radicant will be $49$ and the root will be $7$ .

$\sqrt { Radicand } =Root$

The index usually defines how many times the number should be multiplied to get the original number. In the above examples, the index was taken $2$ that means the number should be multiplied twice by itself to get the original number. Here is a new example with a different index, let's say you are asked to find $\sqrt [ 3 ]{ 8 }$ which means you need to find three factors. If we multiply $2$ three times, it will end up $8$ hence $\sqrt [ 3 ]{ 8 }$ is $2$ .

In simple words, the square root of a number, a, is accurate when a number is found, b, which when elevated to the square is equal to the radicand: ${ b }^{ 2 } = a$