Question

The value of \(\sqrt{(- 25)} + 3\sqrt{(- 4)} + 2\sqrt{(- 9)}\) is equal to

• A. 13i
• B. -13i
• C. 11i
• D. -17i
• E. 17i

Answer 1

Answer: (E)

We are asked to find the value of the expression:

\(\sqrt{-25} + 3\sqrt{-4} + 2\sqrt{-9}\)

We can simplify each square root term by recognizing that the square root of a negative number involves the imaginary unit \(i\), where \(i = \sqrt{-1} \)

1. \(\sqrt{-25} = \sqrt{25} \times \sqrt{-1} = 5i\)

2. \(3\sqrt{-4} = 3 \times \sqrt{4} \times \sqrt{-1} = 3 \times 2 \times i = 6i\)

3. \(2\sqrt{-9} = 2 \times \sqrt{9} \times \sqrt{-1} = 2 \times 3 \times i = 6i\)

Now, combine all the terms:

\(5i + 6i + 6i = 17i\)

The answer is \( 17i \).