Simplify Square Root of 97746

What is the square root of 97746 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.

√97746 = A√B

Unfortunately, the square root of 97746 cannot be simplified. Thus, here is the answer to the square root of 97746 in its simplest form:

√ 97746 = √ 97746

Here are two different methods we used to determine why the square root of 97746 cannot be simplified.

1) To be able to simplify the square root of 97746, one of the factors of 97746 other than 1 must be a perfect square. The factors of 97746 are 1, 2, 3, 6, 11, 22, 33, 66, 1481, 2962, 4443, 8886, 16291, 32582, 48873, and 97746. Since none of these factors are perfect squares, the square root of 97746 cannot be simplified.

2) To be able to simplify the square root of 97746, all the prime factors of 97746 cannot be unique. When we did prime factorization of 97746, we found that 2 x 3 x 11 x 1481 equals 97746. Since all the prime factors are unique, the square root of 97746 cannot be simplified.

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