Simplify Square Root of 4531

What is the square root of 4531 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.

√4531 = A√B

Unfortunately, the square root of 4531 cannot be simplified. Thus, here is the answer to the square root of 4531 in its simplest form:

√ 4531 = √ 4531

Here are two different methods we used to determine why the square root of 4531 cannot be simplified.

1) To be able to simplify the square root of 4531, one of the factors of 4531 other than 1 must be a perfect square. The factors of 4531 are 1, 23, 197, and 4531. Since none of these factors are perfect squares, the square root of 4531 cannot be simplified.

2) To be able to simplify the square root of 4531, all the prime factors of 4531 cannot be unique. When we did prime factorization of 4531, we found that 23 x 197 equals 4531. Since all the prime factors are unique, the square root of 4531 cannot be simplified.

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