Simplify Square Root of 99474

What is the square root of 99474 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.

√99474 = A√B

Unfortunately, the square root of 99474 cannot be simplified. Thus, here is the answer to the square root of 99474 in its simplest form:

√ 99474 = √ 99474

Here are two different methods we used to determine why the square root of 99474 cannot be simplified.

1) To be able to simplify the square root of 99474, one of the factors of 99474 other than 1 must be a perfect square. The factors of 99474 are 1, 2, 3, 6, 59, 118, 177, 281, 354, 562, 843, 1686, 16579, 33158, 49737, and 99474. Since none of these factors are perfect squares, the square root of 99474 cannot be simplified.

2) To be able to simplify the square root of 99474, all the prime factors of 99474 cannot be unique. When we did prime factorization of 99474, we found that 2 x 3 x 59 x 281 equals 99474. Since all the prime factors are unique, the square root of 99474 cannot be simplified.

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