Simplify Square Root of 78673

What is the square root of 78673 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.

√78673 = A√B

Unfortunately, the square root of 78673 cannot be simplified. Thus, here is the answer to the square root of 78673 in its simplest form:

√ 78673 = √ 78673

Here are two different methods we used to determine why the square root of 78673 cannot be simplified.

1) To be able to simplify the square root of 78673, one of the factors of 78673 other than 1 must be a perfect square. The factors of 78673 are 1, 7, 11239, and 78673. Since none of these factors are perfect squares, the square root of 78673 cannot be simplified.

2) To be able to simplify the square root of 78673, all the prime factors of 78673 cannot be unique. When we did prime factorization of 78673, we found that 7 x 11239 equals 78673. Since all the prime factors are unique, the square root of 78673 cannot be simplified.

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