Simplify Square Root of 73461

What is the square root of 73461 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.

√73461 = A√B

Unfortunately, the square root of 73461 cannot be simplified. Thus, here is the answer to the square root of 73461 in its simplest form:

√ 73461 = √ 73461

Here are two different methods we used to determine why the square root of 73461 cannot be simplified.

1) To be able to simplify the square root of 73461, one of the factors of 73461 other than 1 must be a perfect square. The factors of 73461 are 1, 3, 47, 141, 521, 1563, 24487, and 73461. Since none of these factors are perfect squares, the square root of 73461 cannot be simplified.

2) To be able to simplify the square root of 73461, all the prime factors of 73461 cannot be unique. When we did prime factorization of 73461, we found that 3 x 47 x 521 equals 73461. Since all the prime factors are unique, the square root of 73461 cannot be simplified.

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