What is the simplest radical form of 53?

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Do you want to simplify ##sqrt(53)## ?

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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, . . .

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