Find the real-number root √−3.82 show your work

Answer 1

To find the real-number root of √−3.82, we first need to convert -3.82 into a complex number.

Any negative number under a square root is not a real number. To represent it as a complex number, we need to rewrite it as the product of a positive real number and the imaginary unit "i," which is defined as √-1.

So, -3.82 can be written as -3.82 = 3.82 × (-1).

Now, we can rewrite the equation as √(-3.82) = √(3.82 × (-1)).

Taking the square root out of the brackets, we get √(-3.82) = √(3.82) × √(-1).

The square root of 3.82 is a positive real number, but √(-1) is the imaginary unit "i."

Thus, the real-number root of √(-3.82) is √(-3.82) = √(3.82) × √(-1) = √(3.82) × i.