Simplify Square Root of 4573

What is the square root of 4573 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.

√4573 = A√B

Unfortunately, the square root of 4573 cannot be simplified. Thus, here is the answer to the square root of 4573 in its simplest form:

√ 4573 = √ 4573

Here are two different methods we used to determine why the square root of 4573 cannot be simplified.

1) To be able to simplify the square root of 4573, one of the factors of 4573 other than 1 must be a perfect square. The factors of 4573 are 1, 17, 269, and 4573. Since none of these factors are perfect squares, the square root of 4573 cannot be simplified.

2) To be able to simplify the square root of 4573, all the prime factors of 4573 cannot be unique. When we did prime factorization of 4573, we found that 17 x 269 equals 4573. Since all the prime factors are unique, the square root of 4573 cannot be simplified.

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