Simplify Square Root of 7613

What is the square root of 7613 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.

√7613 = A√B

Unfortunately, the square root of 7613 cannot be simplified. Thus, here is the answer to the square root of 7613 in its simplest form:

√ 7613 = √ 7613

Here are two different methods we used to determine why the square root of 7613 cannot be simplified.

1) To be able to simplify the square root of 7613, one of the factors of 7613 other than 1 must be a perfect square. The factors of 7613 are 1, 23, 331, and 7613. Since none of these factors are perfect squares, the square root of 7613 cannot be simplified.

2) To be able to simplify the square root of 7613, all the prime factors of 7613 cannot be unique. When we did prime factorization of 7613, we found that 23 x 331 equals 7613. Since all the prime factors are unique, the square root of 7613 cannot be simplified.

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