Simplify Square Root of 53130

What is the square root of 53130 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.

√53130 = A√B

Unfortunately, the square root of 53130 cannot be simplified. Thus, here is the answer to the square root of 53130 in its simplest form:

√ 53130 = √ 53130

Here are two different methods we used to determine why the square root of 53130 cannot be simplified.

1) To be able to simplify the square root of 53130, one of the factors of 53130 other than 1 must be a perfect square. The factors of 53130 are 1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 23, 30, 33, 35, 42, 46, 55, 66, 69, 70, 77, 105, 110, 115, 138, 154, 161, 165, 210, 230, 231, 253, 322, 330, 345, 385, 462, 483, 506, 690, 759, 770, 805, 966, 1155, 1265, 1518, 1610, 1771, 2310, 2415, 2530, 3542, 3795, 4830, 5313, 7590, 8855, 10626, 17710, 26565, and 53130. Since none of these factors are perfect squares, the square root of 53130 cannot be simplified.

2) To be able to simplify the square root of 53130, all the prime factors of 53130 cannot be unique. When we did prime factorization of 53130, we found that 2 x 3 x 5 x 7 x 11 x 23 equals 53130. Since all the prime factors are unique, the square root of 53130 cannot be simplified.

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