Simplify Square Root of 75877

What is the square root of 75877 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.

√75877 = A√B

Unfortunately, the square root of 75877 cannot be simplified. Thus, here is the answer to the square root of 75877 in its simplest form:

√ 75877 = √ 75877

Here are two different methods we used to determine why the square root of 75877 cannot be simplified.

1) To be able to simplify the square root of 75877, one of the factors of 75877 other than 1 must be a perfect square. The factors of 75877 are 1, 23, 3299, and 75877. Since none of these factors are perfect squares, the square root of 75877 cannot be simplified.

2) To be able to simplify the square root of 75877, all the prime factors of 75877 cannot be unique. When we did prime factorization of 75877, we found that 23 x 3299 equals 75877. Since all the prime factors are unique, the square root of 75877 cannot be simplified.

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