Simplify Square Root of 48405

What is the square root of 48405 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.

√48405 = A√B

Unfortunately, the square root of 48405 cannot be simplified. Thus, here is the answer to the square root of 48405 in its simplest form:

√ 48405 = √ 48405

Here are two different methods we used to determine why the square root of 48405 cannot be simplified.

1) To be able to simplify the square root of 48405, one of the factors of 48405 other than 1 must be a perfect square. The factors of 48405 are 1, 3, 5, 7, 15, 21, 35, 105, 461, 1383, 2305, 3227, 6915, 9681, 16135, and 48405. Since none of these factors are perfect squares, the square root of 48405 cannot be simplified.

2) To be able to simplify the square root of 48405, all the prime factors of 48405 cannot be unique. When we did prime factorization of 48405, we found that 3 x 5 x 7 x 461 equals 48405. Since all the prime factors are unique, the square root of 48405 cannot be simplified.

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