Simplify Square Root of 49153

What is the square root of 49153 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.

√49153 = A√B

Unfortunately, the square root of 49153 cannot be simplified. Thus, here is the answer to the square root of 49153 in its simplest form:

√ 49153 = √ 49153

Here are two different methods we used to determine why the square root of 49153 cannot be simplified.

1) To be able to simplify the square root of 49153, one of the factors of 49153 other than 1 must be a perfect square. The factors of 49153 are 1, 13, 19, 199, 247, 2587, 3781, and 49153. Since none of these factors are perfect squares, the square root of 49153 cannot be simplified.

2) To be able to simplify the square root of 49153, all the prime factors of 49153 cannot be unique. When we did prime factorization of 49153, we found that 13 x 19 x 199 equals 49153. Since all the prime factors are unique, the square root of 49153 cannot be simplified.

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