Simplify Square Root of 48523

What is the square root of 48523 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.

√48523 = A√B

Unfortunately, the square root of 48523 cannot be simplified. Thus, here is the answer to the square root of 48523 in its simplest form:

√ 48523 = √ 48523

Here are two different methods we used to determine why the square root of 48523 cannot be simplified.

1) To be able to simplify the square root of 48523, one of the factors of 48523 other than 1 must be a perfect square. The factors of 48523 are 1 and 48523. Since none of these factors are perfect squares, the square root of 48523 cannot be simplified.

2) To be able to simplify the square root of 48523, all the prime factors of 48523 cannot be unique. When we did prime factorization of 48523, we found that 48523 equals 48523. Since all the prime factors are unique, the square root of 48523 cannot be simplified.

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