Square root of -45 = (-45)1/2 = (-3x3x5)1/2 = 3(-5)1/2 = 351/2i
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Square roots of negative numbers are what are called imaginary numbers. The building block of imaginary numbers is the symbol i which is defined as the square root of negative 1. The square root of other negative numbers can be expressed using i. For example, the square root of negative sixteen is 4i, the square root of negative nine is 3i and so on.
Negative numbers do not have "real number" square roots.However, they will have two roots (when using imaginary numbers) as do other numbers, where a root including i(square root of -1) is positive or negative.
4 times the square root of 5. it's undefinable so that's the most you can simplify it without using imaginary numbers
Not in the case of Rational Numbers -- only in Imaginary Numbers, typically referring to the imaginary component.
The square root of a negative number is considered an imaginary number. In this case, the square root of -2 is represented as √(-2) = √2i, where i is the imaginary unit equal to the square root of -1. This is because the square root of -1 is not a real number, so we introduce the concept of imaginary numbers to handle such cases in mathematics.