Simplify Square Root of 45418

What is the square root of 45418 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.

√45418 = A√B

Unfortunately, the square root of 45418 cannot be simplified. Thus, here is the answer to the square root of 45418 in its simplest form:

√ 45418 = √ 45418

Here are two different methods we used to determine why the square root of 45418 cannot be simplified.

1) To be able to simplify the square root of 45418, one of the factors of 45418 other than 1 must be a perfect square. The factors of 45418 are 1, 2, 22709, and 45418. Since none of these factors are perfect squares, the square root of 45418 cannot be simplified.

2) To be able to simplify the square root of 45418, all the prime factors of 45418 cannot be unique. When we did prime factorization of 45418, we found that 2 x 22709 equals 45418. Since all the prime factors are unique, the square root of 45418 cannot be simplified.

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