Simplify Square Root of 71746

What is the square root of 71746 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.

√71746 = A√B

Unfortunately, the square root of 71746 cannot be simplified. Thus, here is the answer to the square root of 71746 in its simplest form:

√ 71746 = √ 71746

Here are two different methods we used to determine why the square root of 71746 cannot be simplified.

1) To be able to simplify the square root of 71746, one of the factors of 71746 other than 1 must be a perfect square. The factors of 71746 are 1, 2, 29, 58, 1237, 2474, 35873, and 71746. Since none of these factors are perfect squares, the square root of 71746 cannot be simplified.

2) To be able to simplify the square root of 71746, all the prime factors of 71746 cannot be unique. When we did prime factorization of 71746, we found that 2 x 29 x 1237 equals 71746. Since all the prime factors are unique, the square root of 71746 cannot be simplified.

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