Simplify Square Root of 35763

What is the square root of 35763 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.

√35763 = A√B

Unfortunately, the square root of 35763 cannot be simplified. Thus, here is the answer to the square root of 35763 in its simplest form:

√ 35763 = √ 35763

Here are two different methods we used to determine why the square root of 35763 cannot be simplified.

1) To be able to simplify the square root of 35763, one of the factors of 35763 other than 1 must be a perfect square. The factors of 35763 are 1, 3, 7, 13, 21, 39, 91, 131, 273, 393, 917, 1703, 2751, 5109, 11921, and 35763. Since none of these factors are perfect squares, the square root of 35763 cannot be simplified.

2) To be able to simplify the square root of 35763, all the prime factors of 35763 cannot be unique. When we did prime factorization of 35763, we found that 3 x 7 x 13 x 131 equals 35763. Since all the prime factors are unique, the square root of 35763 cannot be simplified.

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