# What is the simplest radical form of 53?

Aug 26, 2016

Do you want to simplify $\sqrt{53}$ ?

#### Explanation:

What prime factors divide 53? 53 itself looks prime to me.

In order to simplify $53$ and then take the square root, you have to be able to factor 53 into smaller numbers, at least one of which is a perfect square.

For example, what is $\sqrt{144}$ ?
144 can be factored into 12 x 12 or ${12}^{2}$.
So you have $\sqrt{{12}^{2}}$ which is $12$ .

How about $\sqrt{20}$ ?
First, factor 20 as 5 x 4.
Then write 4 as ${2}^{2}$ .
You have $\sqrt{{2}^{2} \cdot 5}$, which equals $\sqrt{{2}^{2}} \cdot \sqrt{5}$, which equals $2 \sqrt{5}$.

I think that's what you want to do with $\sqrt{53}$, except you can't, because 53 can only be divided by itself and one - it's prime.

The simplest form of $\sqrt{53}$ is $\sqrt{53}$.

Here are the first 18 prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, . . .