Simplify Square Root of 23519

What is the square root of 23519 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.

√23519 = A√B

Unfortunately, the square root of 23519 cannot be simplified. Thus, here is the answer to the square root of 23519 in its simplest form:

√ 23519 = √ 23519

Here are two different methods we used to determine why the square root of 23519 cannot be simplified.

1) To be able to simplify the square root of 23519, one of the factors of 23519 other than 1 must be a perfect square. The factors of 23519 are 1, 29, 811, and 23519. Since none of these factors are perfect squares, the square root of 23519 cannot be simplified.

2) To be able to simplify the square root of 23519, all the prime factors of 23519 cannot be unique. When we did prime factorization of 23519, we found that 29 x 811 equals 23519. Since all the prime factors are unique, the square root of 23519 cannot be simplified.

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