Simplify Square Root of 11510

What is the square root of 11510 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.

√11510 = A√B

Unfortunately, the square root of 11510 cannot be simplified. Thus, here is the answer to the square root of 11510 in its simplest form:

√ 11510 = √ 11510

Here are two different methods we used to determine why the square root of 11510 cannot be simplified.

1) To be able to simplify the square root of 11510, one of the factors of 11510 other than 1 must be a perfect square. The factors of 11510 are 1, 2, 5, 10, 1151, 2302, 5755, and 11510. Since none of these factors are perfect squares, the square root of 11510 cannot be simplified.

2) To be able to simplify the square root of 11510, all the prime factors of 11510 cannot be unique. When we did prime factorization of 11510, we found that 2 x 5 x 1151 equals 11510. Since all the prime factors are unique, the square root of 11510 cannot be simplified.

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