Math Problem Statement

Which of the following is the square root of -16?

Solution

The question is asking for the square root of 16-16.

To solve this, recall that the square root of a negative number involves imaginary numbers. The square root of 1-1 is represented by the imaginary unit ii, where:

i=1i = \sqrt{-1}

For 16-16, we break it down as follows:

16=16×1=4i\sqrt{-16} = \sqrt{16} \times \sqrt{-1} = 4i

Thus, the square root of 16-16 is 4i4i.

The correct answer is 4i4i (the last option).

Would you like further details or have any questions?

Here are five related questions for further practice:

  1. What is the square root of 25-25?
  2. How do you simplify 9\sqrt{-9}?
  3. What is the value of i2i^2?
  4. How do you multiply two complex numbers involving ii?
  5. What is the meaning of an imaginary number?

Tip: When dealing with square roots of negative numbers, always remember that they involve imaginary numbers, represented by ii.

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Math Problem Analysis

Mathematical Concepts

Imaginary Numbers
Square Roots of Negative Numbers

Formulas

i = √(-1)
√(-16) = √(16) × √(-1) = 4i

Theorems

Square root of negative numbers theorem

Suitable Grade Level

Grades 9-12