Simplify Square Root of 65753

What is the square root of 65753 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.

√65753 = A√B

Unfortunately, the square root of 65753 cannot be simplified. Thus, here is the answer to the square root of 65753 in its simplest form:

√ 65753 = √ 65753

Here are two different methods we used to determine why the square root of 65753 cannot be simplified.

1) To be able to simplify the square root of 65753, one of the factors of 65753 other than 1 must be a perfect square. The factors of 65753 are 1, 47, 1399, and 65753. Since none of these factors are perfect squares, the square root of 65753 cannot be simplified.

2) To be able to simplify the square root of 65753, all the prime factors of 65753 cannot be unique. When we did prime factorization of 65753, we found that 47 x 1399 equals 65753. Since all the prime factors are unique, the square root of 65753 cannot be simplified.

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