Simplify Square Root of 45267

What is the square root of 45267 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.

√45267 = A√B

Unfortunately, the square root of 45267 cannot be simplified. Thus, here is the answer to the square root of 45267 in its simplest form:

√ 45267 = √ 45267

Here are two different methods we used to determine why the square root of 45267 cannot be simplified.

1) To be able to simplify the square root of 45267, one of the factors of 45267 other than 1 must be a perfect square. The factors of 45267 are 1, 3, 79, 191, 237, 573, 15089, and 45267. Since none of these factors are perfect squares, the square root of 45267 cannot be simplified.

2) To be able to simplify the square root of 45267, all the prime factors of 45267 cannot be unique. When we did prime factorization of 45267, we found that 3 x 79 x 191 equals 45267. Since all the prime factors are unique, the square root of 45267 cannot be simplified.

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