Simplify Square Root of 14777

What is the square root of 14777 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.

√14777 = A√B

Unfortunately, the square root of 14777 cannot be simplified. Thus, here is the answer to the square root of 14777 in its simplest form:

√ 14777 = √ 14777

Here are two different methods we used to determine why the square root of 14777 cannot be simplified.

1) To be able to simplify the square root of 14777, one of the factors of 14777 other than 1 must be a perfect square. The factors of 14777 are 1, 7, 2111, and 14777. Since none of these factors are perfect squares, the square root of 14777 cannot be simplified.

2) To be able to simplify the square root of 14777, all the prime factors of 14777 cannot be unique. When we did prime factorization of 14777, we found that 7 x 2111 equals 14777. Since all the prime factors are unique, the square root of 14777 cannot be simplified.

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