What is the simplest radical form of 53?

1 Answer
Aug 26, 2016

Answer:

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, . . .