Simplify Square Root of 78473

What is the square root of 78473 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.

√78473 = A√B

Unfortunately, the square root of 78473 cannot be simplified. Thus, here is the answer to the square root of 78473 in its simplest form:

√ 78473 = √ 78473

Here are two different methods we used to determine why the square root of 78473 cannot be simplified.

1) To be able to simplify the square root of 78473, one of the factors of 78473 other than 1 must be a perfect square. The factors of 78473 are 1, 97, 809, and 78473. Since none of these factors are perfect squares, the square root of 78473 cannot be simplified.

2) To be able to simplify the square root of 78473, all the prime factors of 78473 cannot be unique. When we did prime factorization of 78473, we found that 97 x 809 equals 78473. Since all the prime factors are unique, the square root of 78473 cannot be simplified.

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