Simplify Square Root of 73641

What is the square root of 73641 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.

√73641 = A√B

Unfortunately, the square root of 73641 cannot be simplified. Thus, here is the answer to the square root of 73641 in its simplest form:

√ 73641 = √ 73641

Here are two different methods we used to determine why the square root of 73641 cannot be simplified.

1) To be able to simplify the square root of 73641, one of the factors of 73641 other than 1 must be a perfect square. The factors of 73641 are 1, 3, 24547, and 73641. Since none of these factors are perfect squares, the square root of 73641 cannot be simplified.

2) To be able to simplify the square root of 73641, all the prime factors of 73641 cannot be unique. When we did prime factorization of 73641, we found that 3 x 24547 equals 73641. Since all the prime factors are unique, the square root of 73641 cannot be simplified.

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