Simplify Square Root of 1121

What is the square root of 1121 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.

√1121 = A√B

Unfortunately, the square root of 1121 cannot be simplified. Thus, here is the answer to the square root of 1121 in its simplest form:

√ 1121 = √ 1121

Here are two different methods we used to determine why the square root of 1121 cannot be simplified.

1) To be able to simplify the square root of 1121, one of the factors of 1121 other than 1 must be a perfect square. The factors of 1121 are 1, 19, 59, and 1121. Since none of these factors are perfect squares, the square root of 1121 cannot be simplified.

2) To be able to simplify the square root of 1121, all the prime factors of 1121 cannot be unique. When we did prime factorization of 1121, we found that 19 x 59 equals 1121. Since all the prime factors are unique, the square root of 1121 cannot be simplified.

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