Simplify Square Root of 15755

What is the square root of 15755 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.

√15755 = A√B

Unfortunately, the square root of 15755 cannot be simplified. Thus, here is the answer to the square root of 15755 in its simplest form:

√ 15755 = √ 15755

Here are two different methods we used to determine why the square root of 15755 cannot be simplified.

1) To be able to simplify the square root of 15755, one of the factors of 15755 other than 1 must be a perfect square. The factors of 15755 are 1, 5, 23, 115, 137, 685, 3151, and 15755. Since none of these factors are perfect squares, the square root of 15755 cannot be simplified.

2) To be able to simplify the square root of 15755, all the prime factors of 15755 cannot be unique. When we did prime factorization of 15755, we found that 5 x 23 x 137 equals 15755. Since all the prime factors are unique, the square root of 15755 cannot be simplified.

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