Taking the square root of an atomic number is not particularly useful. Anyway, you can look up the atomic number in a periodic table or some other reference material (searching Wikipedia for "manganese" should work well), and then use a calculator to take the square root.
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It means you are finding what number multiplied by itself will give you the number you are finding the square root of.
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If you are trying to find the number of square units on the surface of something, you find the area of that surface (the width times the height). The answer is written as units2
Finding the square root of a number is performing the opposite operation of squaring the number. In order to square a number you must multiple the number by itself. 2 x 2 = 4 so the square root of 4 is 2.