Simplify Square Root of 48914

What is the square root of 48914 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.

√48914 = A√B

Unfortunately, the square root of 48914 cannot be simplified. Thus, here is the answer to the square root of 48914 in its simplest form:

√ 48914 = √ 48914

Here are two different methods we used to determine why the square root of 48914 cannot be simplified.

1) To be able to simplify the square root of 48914, one of the factors of 48914 other than 1 must be a perfect square. The factors of 48914 are 1, 2, 37, 74, 661, 1322, 24457, and 48914. Since none of these factors are perfect squares, the square root of 48914 cannot be simplified.

2) To be able to simplify the square root of 48914, all the prime factors of 48914 cannot be unique. When we did prime factorization of 48914, we found that 2 x 37 x 661 equals 48914. Since all the prime factors are unique, the square root of 48914 cannot be simplified.

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