Simplify Square Root of 23230

What is the square root of 23230 in its simplest radical form? To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√23230 = A√B

Unfortunately, the square root of 23230 cannot be simplified. Thus, here is the answer to the square root of 23230 in its simplest form:

√ 23230 = √ 23230

Here are two different methods we used to determine why the square root of 23230 cannot be simplified.

1) To be able to simplify the square root of 23230, one of the factors of 23230 other than 1 must be a perfect square. The factors of 23230 are 1, 2, 5, 10, 23, 46, 101, 115, 202, 230, 505, 1010, 2323, 4646, 11615, and 23230. Since none of these factors are perfect squares, the square root of 23230 cannot be simplified.

2) To be able to simplify the square root of 23230, all the prime factors of 23230 cannot be unique. When we did prime factorization of 23230, we found that 2 x 5 x 23 x 101 equals 23230. Since all the prime factors are unique, the square root of 23230 cannot be simplified.

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