Simplify Square Root of 73670

What is the square root of 73670 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.

√73670 = A√B

Unfortunately, the square root of 73670 cannot be simplified. Thus, here is the answer to the square root of 73670 in its simplest form:

√ 73670 = √ 73670

Here are two different methods we used to determine why the square root of 73670 cannot be simplified.

1) To be able to simplify the square root of 73670, one of the factors of 73670 other than 1 must be a perfect square. The factors of 73670 are 1, 2, 5, 10, 53, 106, 139, 265, 278, 530, 695, 1390, 7367, 14734, 36835, and 73670. Since none of these factors are perfect squares, the square root of 73670 cannot be simplified.

2) To be able to simplify the square root of 73670, all the prime factors of 73670 cannot be unique. When we did prime factorization of 73670, we found that 2 x 5 x 53 x 139 equals 73670. Since all the prime factors are unique, the square root of 73670 cannot be simplified.

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