Simplify Square Root of 45010

What is the square root of 45010 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.

√45010 = A√B

Unfortunately, the square root of 45010 cannot be simplified. Thus, here is the answer to the square root of 45010 in its simplest form:

√ 45010 = √ 45010

Here are two different methods we used to determine why the square root of 45010 cannot be simplified.

1) To be able to simplify the square root of 45010, one of the factors of 45010 other than 1 must be a perfect square. The factors of 45010 are 1, 2, 5, 7, 10, 14, 35, 70, 643, 1286, 3215, 4501, 6430, 9002, 22505, and 45010. Since none of these factors are perfect squares, the square root of 45010 cannot be simplified.

2) To be able to simplify the square root of 45010, all the prime factors of 45010 cannot be unique. When we did prime factorization of 45010, we found that 2 x 5 x 7 x 643 equals 45010. Since all the prime factors are unique, the square root of 45010 cannot be simplified.

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