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ippStsSqrtNegArg
Numbers multiplied by themselves, such as 3 times 3, 25 times 25, or 4 times 4 times 4, belong to a special class of numbers. The numbers used to multiply themselves are called roots, and the number of times they multiply themselves have their own names. The number 4 is the cubed root, or 43, of 64, because the number 4 is used as a factor three times to get 64, with no other numbers used. A number like 16 can be written as 4x4, which makes the number four its square root, as the number 4 is its two products. The word square here means a number is multiplied by itself. It can also be called the root number, or index, of two. When finding the square root of a number a special symbol is used--the square root sign. The number under the sign is called the radicand. The square root sign and number beneath it is referred to as a radical. With no number before it, we are looking for a simple square.
Can a Square Root be Negative?
Although square roots are generally taken to be positive, a square root can be negative as a negative number multiplied by a negative number is always positive.
What Is a Negative Square Root?
In general, when someone is asking for a square root, they are seeking the positive value. This is called the principal square root. However, square roots can also be negative. Thus, the number -6 can be a square root of the number 36, just not a principal square root. So the negative square root is the same number as the principal square root, but the negative version. The negative square "squared" will give the same positive result as the principal square root, for instance, 3⋅3=9 and -3 ⋅ -3 = 9.
Can You Square Root a Negative Number?
So, is there a way of taking the square root of negative numbers? Theoretically, using real numbers, it cannot be done. Two negative numbers multiplied together always produce a positive number; there are no known exceptions. The number zero is considered to be its own square root. However, mathematicians have found a way to calculate square roots of negative numbers. Any negative number can be written as a multiple of -1.