Simplify Square Root of 75310

What is the square root of 75310 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.

√75310 = A√B

Unfortunately, the square root of 75310 cannot be simplified. Thus, here is the answer to the square root of 75310 in its simplest form:

√ 75310 = √ 75310

Here are two different methods we used to determine why the square root of 75310 cannot be simplified.

1) To be able to simplify the square root of 75310, one of the factors of 75310 other than 1 must be a perfect square. The factors of 75310 are 1, 2, 5, 10, 17, 34, 85, 170, 443, 886, 2215, 4430, 7531, 15062, 37655, and 75310. Since none of these factors are perfect squares, the square root of 75310 cannot be simplified.

2) To be able to simplify the square root of 75310, all the prime factors of 75310 cannot be unique. When we did prime factorization of 75310, we found that 2 x 5 x 17 x 443 equals 75310. Since all the prime factors are unique, the square root of 75310 cannot be simplified.

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