Simplify Square Root of 9847

What is the square root of 9847 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.

√9847 = A√B

Unfortunately, the square root of 9847 cannot be simplified. Thus, here is the answer to the square root of 9847 in its simplest form:

√ 9847 = √ 9847

Here are two different methods we used to determine why the square root of 9847 cannot be simplified.

1) To be able to simplify the square root of 9847, one of the factors of 9847 other than 1 must be a perfect square. The factors of 9847 are 1, 43, 229, and 9847. Since none of these factors are perfect squares, the square root of 9847 cannot be simplified.

2) To be able to simplify the square root of 9847, all the prime factors of 9847 cannot be unique. When we did prime factorization of 9847, we found that 43 x 229 equals 9847. Since all the prime factors are unique, the square root of 9847 cannot be simplified.

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