Simplify Square Root of 36773

What is the square root of 36773 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.

√36773 = A√B

Unfortunately, the square root of 36773 cannot be simplified. Thus, here is the answer to the square root of 36773 in its simplest form:

√ 36773 = √ 36773

Here are two different methods we used to determine why the square root of 36773 cannot be simplified.

1) To be able to simplify the square root of 36773, one of the factors of 36773 other than 1 must be a perfect square. The factors of 36773 are 1, 11, 3343, and 36773. Since none of these factors are perfect squares, the square root of 36773 cannot be simplified.

2) To be able to simplify the square root of 36773, all the prime factors of 36773 cannot be unique. When we did prime factorization of 36773, we found that 11 x 3343 equals 36773. Since all the prime factors are unique, the square root of 36773 cannot be simplified.

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