Simplify Square Root of 48493

What is the square root of 48493 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.

√48493 = A√B

Unfortunately, the square root of 48493 cannot be simplified. Thus, here is the answer to the square root of 48493 in its simplest form:

√ 48493 = √ 48493

Here are two different methods we used to determine why the square root of 48493 cannot be simplified.

1) To be able to simplify the square root of 48493, one of the factors of 48493 other than 1 must be a perfect square. The factors of 48493 are 1, 71, 683, and 48493. Since none of these factors are perfect squares, the square root of 48493 cannot be simplified.

2) To be able to simplify the square root of 48493, all the prime factors of 48493 cannot be unique. When we did prime factorization of 48493, we found that 71 x 683 equals 48493. Since all the prime factors are unique, the square root of 48493 cannot be simplified.

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