Simplify Square Root of 30290

What is the square root of 30290 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.

√30290 = A√B

Unfortunately, the square root of 30290 cannot be simplified. Thus, here is the answer to the square root of 30290 in its simplest form:

√ 30290 = √ 30290

Here are two different methods we used to determine why the square root of 30290 cannot be simplified.

1) To be able to simplify the square root of 30290, one of the factors of 30290 other than 1 must be a perfect square. The factors of 30290 are 1, 2, 5, 10, 13, 26, 65, 130, 233, 466, 1165, 2330, 3029, 6058, 15145, and 30290. Since none of these factors are perfect squares, the square root of 30290 cannot be simplified.

2) To be able to simplify the square root of 30290, all the prime factors of 30290 cannot be unique. When we did prime factorization of 30290, we found that 2 x 5 x 13 x 233 equals 30290. Since all the prime factors are unique, the square root of 30290 cannot be simplified.

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