Simplify Square Root of 29522

What is the square root of 29522 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.

√29522 = A√B

Unfortunately, the square root of 29522 cannot be simplified. Thus, here is the answer to the square root of 29522 in its simplest form:

√ 29522 = √ 29522

Here are two different methods we used to determine why the square root of 29522 cannot be simplified.

1) To be able to simplify the square root of 29522, one of the factors of 29522 other than 1 must be a perfect square. The factors of 29522 are 1, 2, 29, 58, 509, 1018, 14761, and 29522. Since none of these factors are perfect squares, the square root of 29522 cannot be simplified.

2) To be able to simplify the square root of 29522, all the prime factors of 29522 cannot be unique. When we did prime factorization of 29522, we found that 2 x 29 x 509 equals 29522. Since all the prime factors are unique, the square root of 29522 cannot be simplified.

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