Simplify Square Root of 70178

What is the square root of 70178 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.

√70178 = A√B

Unfortunately, the square root of 70178 cannot be simplified. Thus, here is the answer to the square root of 70178 in its simplest form:

√ 70178 = √ 70178

Here are two different methods we used to determine why the square root of 70178 cannot be simplified.

1) To be able to simplify the square root of 70178, one of the factors of 70178 other than 1 must be a perfect square. The factors of 70178 are 1, 2, 35089, and 70178. Since none of these factors are perfect squares, the square root of 70178 cannot be simplified.

2) To be able to simplify the square root of 70178, all the prime factors of 70178 cannot be unique. When we did prime factorization of 70178, we found that 2 x 35089 equals 70178. Since all the prime factors are unique, the square root of 70178 cannot be simplified.

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