Simplify Square Root of 45633

What is the square root of 45633 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.

√45633 = A√B

Unfortunately, the square root of 45633 cannot be simplified. Thus, here is the answer to the square root of 45633 in its simplest form:

√ 45633 = √ 45633

Here are two different methods we used to determine why the square root of 45633 cannot be simplified.

1) To be able to simplify the square root of 45633, one of the factors of 45633 other than 1 must be a perfect square. The factors of 45633 are 1, 3, 7, 21, 41, 53, 123, 159, 287, 371, 861, 1113, 2173, 6519, 15211, and 45633. Since none of these factors are perfect squares, the square root of 45633 cannot be simplified.

2) To be able to simplify the square root of 45633, all the prime factors of 45633 cannot be unique. When we did prime factorization of 45633, we found that 3 x 7 x 41 x 53 equals 45633. Since all the prime factors are unique, the square root of 45633 cannot be simplified.

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