Question

What is the simplest radical form of 53?

Answer 1

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*5)`, which equals `sqrt(2^2)*sqrt(5)`, which equals `2sqrt(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, . . .