Math Problem Statement

Evaluate the expression √-16 and write the result in the form a+bi .

Solution

The expression 16\sqrt{-16} involves taking the square root of a negative number, which requires using imaginary numbers. We know that:

1=i\sqrt{-1} = i

Thus, 16\sqrt{-16} can be rewritten as:

16=16(1)=161=4i\sqrt{-16} = \sqrt{16 \cdot (-1)} = \sqrt{16} \cdot \sqrt{-1} = 4i

So, the result in the form a+bia + bi is:

0+4i0 + 4i

Would you like further explanation or details?

Here are 5 related questions for practice:

  1. What is 9\sqrt{-9} in the form a+bia + bi?
  2. How do you simplify 25\sqrt{-25}?
  3. What is 1\sqrt{-1} known as?
  4. Convert 36\sqrt{-36} to the form a+bia + bi.
  5. How do you handle square roots of negative numbers in general?

Tip: When dealing with square roots of negative numbers, always factor out 1=i\sqrt{-1} = i first!

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Math Problem Analysis

Mathematical Concepts

Imaginary Numbers
Complex Numbers
Square Roots of Negative Numbers

Formulas

√-1 = i
√(a * b) = √a * √b

Theorems

Properties of Imaginary Numbers

Suitable Grade Level

Grades 8-10