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### Square root

The square root of the number *a* means looking for a number that when squared gives *a*. You write it as

##### Explanation

Here we have the well known 2^{nd} root, called the square root. On your calculator you can see

There is also a 3^{rd}, 4^{th} and also a *n*^{th} root. It always works in the same manner

and so

It only gets difficult if you cannot easily factorize the value. Nevertheless, you can calculate with roots, as it are just numbers

but it is not possible to do this manually. You can write roots as powers

and this explains what a root really is, as

Now we multiply roots

When dividing, we avoid having roots in the denominator

and that looks better. Now we make it more difficult and write

We verify this, and take *a = *64, because the answer will be

We use the original formula and find

So it works.