Simplify Square Root of 89501

What is the square root of 89501 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.

√89501 = A√B

Unfortunately, the square root of 89501 cannot be simplified. Thus, here is the answer to the square root of 89501 in its simplest form:

√ 89501 = √ 89501

Here are two different methods we used to determine why the square root of 89501 cannot be simplified.

1) To be able to simplify the square root of 89501, one of the factors of 89501 other than 1 must be a perfect square. The factors of 89501 are 1 and 89501. Since none of these factors are perfect squares, the square root of 89501 cannot be simplified.

2) To be able to simplify the square root of 89501, all the prime factors of 89501 cannot be unique. When we did prime factorization of 89501, we found that 89501 equals 89501. Since all the prime factors are unique, the square root of 89501 cannot be simplified.

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