Simplify Square Root of 1561

What is the square root of 1561 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.

√1561 = A√B

Unfortunately, the square root of 1561 cannot be simplified. Thus, here is the answer to the square root of 1561 in its simplest form:

√ 1561 = √ 1561

Here are two different methods we used to determine why the square root of 1561 cannot be simplified.

1) To be able to simplify the square root of 1561, one of the factors of 1561 other than 1 must be a perfect square. The factors of 1561 are 1, 7, 223, and 1561. Since none of these factors are perfect squares, the square root of 1561 cannot be simplified.

2) To be able to simplify the square root of 1561, all the prime factors of 1561 cannot be unique. When we did prime factorization of 1561, we found that 7 x 223 equals 1561. Since all the prime factors are unique, the square root of 1561 cannot be simplified.

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