Simplify Square Root of 35761

What is the square root of 35761 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.

√35761 = A√B

Unfortunately, the square root of 35761 cannot be simplified. Thus, here is the answer to the square root of 35761 in its simplest form:

√ 35761 = √ 35761

Here are two different methods we used to determine why the square root of 35761 cannot be simplified.

1) To be able to simplify the square root of 35761, one of the factors of 35761 other than 1 must be a perfect square. The factors of 35761 are 1, 11, 3251, and 35761. Since none of these factors are perfect squares, the square root of 35761 cannot be simplified.

2) To be able to simplify the square root of 35761, all the prime factors of 35761 cannot be unique. When we did prime factorization of 35761, we found that 11 x 3251 equals 35761. Since all the prime factors are unique, the square root of 35761 cannot be simplified.

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