Simplify Square Root of 99314

What is the square root of 99314 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.

√99314 = A√B

Unfortunately, the square root of 99314 cannot be simplified. Thus, here is the answer to the square root of 99314 in its simplest form:

√ 99314 = √ 99314

Here are two different methods we used to determine why the square root of 99314 cannot be simplified.

1) To be able to simplify the square root of 99314, one of the factors of 99314 other than 1 must be a perfect square. The factors of 99314 are 1, 2, 17, 23, 34, 46, 127, 254, 391, 782, 2159, 2921, 4318, 5842, 49657, and 99314. Since none of these factors are perfect squares, the square root of 99314 cannot be simplified.

2) To be able to simplify the square root of 99314, all the prime factors of 99314 cannot be unique. When we did prime factorization of 99314, we found that 2 x 17 x 23 x 127 equals 99314. Since all the prime factors are unique, the square root of 99314 cannot be simplified.

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