Simplify Square Root of 1545

What is the square root of 1545 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.

√1545 = A√B

Unfortunately, the square root of 1545 cannot be simplified. Thus, here is the answer to the square root of 1545 in its simplest form:

√ 1545 = √ 1545

Here are two different methods we used to determine why the square root of 1545 cannot be simplified.

1) To be able to simplify the square root of 1545, one of the factors of 1545 other than 1 must be a perfect square. The factors of 1545 are 1, 3, 5, 15, 103, 309, 515, and 1545. Since none of these factors are perfect squares, the square root of 1545 cannot be simplified.

2) To be able to simplify the square root of 1545, all the prime factors of 1545 cannot be unique. When we did prime factorization of 1545, we found that 3 x 5 x 103 equals 1545. Since all the prime factors are unique, the square root of 1545 cannot be simplified.

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