Simplify Square Root of 73617

What is the square root of 73617 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.

√73617 = A√B

Unfortunately, the square root of 73617 cannot be simplified. Thus, here is the answer to the square root of 73617 in its simplest form:

√ 73617 = √ 73617

Here are two different methods we used to determine why the square root of 73617 cannot be simplified.

1) To be able to simplify the square root of 73617, one of the factors of 73617 other than 1 must be a perfect square. The factors of 73617 are 1, 3, 53, 159, 463, 1389, 24539, and 73617. Since none of these factors are perfect squares, the square root of 73617 cannot be simplified.

2) To be able to simplify the square root of 73617, all the prime factors of 73617 cannot be unique. When we did prime factorization of 73617, we found that 3 x 53 x 463 equals 73617. Since all the prime factors are unique, the square root of 73617 cannot be simplified.

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