Simplify Square Root of 19523

What is the square root of 19523 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.

√19523 = A√B

Unfortunately, the square root of 19523 cannot be simplified. Thus, here is the answer to the square root of 19523 in its simplest form:

√ 19523 = √ 19523

Here are two different methods we used to determine why the square root of 19523 cannot be simplified.

1) To be able to simplify the square root of 19523, one of the factors of 19523 other than 1 must be a perfect square. The factors of 19523 are 1, 7, 2789, and 19523. Since none of these factors are perfect squares, the square root of 19523 cannot be simplified.

2) To be able to simplify the square root of 19523, all the prime factors of 19523 cannot be unique. When we did prime factorization of 19523, we found that 7 x 2789 equals 19523. Since all the prime factors are unique, the square root of 19523 cannot be simplified.

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