Simplify Square Root of 75153

What is the square root of 75153 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.

√75153 = A√B

Unfortunately, the square root of 75153 cannot be simplified. Thus, here is the answer to the square root of 75153 in its simplest form:

√ 75153 = √ 75153

Here are two different methods we used to determine why the square root of 75153 cannot be simplified.

1) To be able to simplify the square root of 75153, one of the factors of 75153 other than 1 must be a perfect square. The factors of 75153 are 1, 3, 13, 39, 41, 47, 123, 141, 533, 611, 1599, 1833, 1927, 5781, 25051, and 75153. Since none of these factors are perfect squares, the square root of 75153 cannot be simplified.

2) To be able to simplify the square root of 75153, all the prime factors of 75153 cannot be unique. When we did prime factorization of 75153, we found that 3 x 13 x 41 x 47 equals 75153. Since all the prime factors are unique, the square root of 75153 cannot be simplified.

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