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### Root

**Extracting the root** from a number *a* means searching for a number that gives *a* when squared. You write it as

##### Explanation

This is the famous 2^{nd} root, the square root. On your calculator you can see

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

and thus

It only gets difficult if you cannot easily factorize the number. Anyhow you can make calculations with roots, as they are just numbers. So

but you need a calculator for that. Roots can be written as exponential functions

and this explains what a root really is, as

Now we multiply roots

During a division we want to avoid roots in the denominator, so

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

We check this, and take *a = *64, sothat the answer will be

We use the original formula and find

So it works.