Simplify Square Root of 68101

What is the square root of 68101 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.

√68101 = A√B

Unfortunately, the square root of 68101 cannot be simplified. Thus, here is the answer to the square root of 68101 in its simplest form:

√ 68101 = √ 68101

Here are two different methods we used to determine why the square root of 68101 cannot be simplified.

1) To be able to simplify the square root of 68101, one of the factors of 68101 other than 1 must be a perfect square. The factors of 68101 are 1, 11, 41, 151, 451, 1661, 6191, and 68101. Since none of these factors are perfect squares, the square root of 68101 cannot be simplified.

2) To be able to simplify the square root of 68101, all the prime factors of 68101 cannot be unique. When we did prime factorization of 68101, we found that 11 x 41 x 151 equals 68101. Since all the prime factors are unique, the square root of 68101 cannot be simplified.

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