Simplify Square Root of 48658

What is the square root of 48658 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.

√48658 = A√B

Unfortunately, the square root of 48658 cannot be simplified. Thus, here is the answer to the square root of 48658 in its simplest form:

√ 48658 = √ 48658

Here are two different methods we used to determine why the square root of 48658 cannot be simplified.

1) To be able to simplify the square root of 48658, one of the factors of 48658 other than 1 must be a perfect square. The factors of 48658 are 1, 2, 24329, and 48658. Since none of these factors are perfect squares, the square root of 48658 cannot be simplified.

2) To be able to simplify the square root of 48658, all the prime factors of 48658 cannot be unique. When we did prime factorization of 48658, we found that 2 x 24329 equals 48658. Since all the prime factors are unique, the square root of 48658 cannot be simplified.

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