Simplify Square Root of 19353

What is the square root of 19353 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.

√19353 = A√B

Unfortunately, the square root of 19353 cannot be simplified. Thus, here is the answer to the square root of 19353 in its simplest form:

√ 19353 = √ 19353

Here are two different methods we used to determine why the square root of 19353 cannot be simplified.

1) To be able to simplify the square root of 19353, one of the factors of 19353 other than 1 must be a perfect square. The factors of 19353 are 1, 3, 6451, and 19353. Since none of these factors are perfect squares, the square root of 19353 cannot be simplified.

2) To be able to simplify the square root of 19353, all the prime factors of 19353 cannot be unique. When we did prime factorization of 19353, we found that 3 x 6451 equals 19353. Since all the prime factors are unique, the square root of 19353 cannot be simplified.

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