Simplify Square Root of 70806

What is the square root of 70806 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.

√70806 = A√B

Unfortunately, the square root of 70806 cannot be simplified. Thus, here is the answer to the square root of 70806 in its simplest form:

√ 70806 = √ 70806

Here are two different methods we used to determine why the square root of 70806 cannot be simplified.

1) To be able to simplify the square root of 70806, one of the factors of 70806 other than 1 must be a perfect square. The factors of 70806 are 1, 2, 3, 6, 11801, 23602, 35403, and 70806. Since none of these factors are perfect squares, the square root of 70806 cannot be simplified.

2) To be able to simplify the square root of 70806, all the prime factors of 70806 cannot be unique. When we did prime factorization of 70806, we found that 2 x 3 x 11801 equals 70806. Since all the prime factors are unique, the square root of 70806 cannot be simplified.

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