Subtract 75–√−45–√.(1 point)

Question

The difference is .

Answer 1

To calculate \( 75 - \sqrt{-45} \), we first simplify \( \sqrt{-45} \).

1. Recall that \( \sqrt{-a} = i\sqrt{a} \), where \( i \) is the imaginary unit.
2. So, \( \sqrt{-45} = \sqrt{45}i \).
3. Now, simplify \( \sqrt{45} \):
   • \( \sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5} \).

Thus, \( \sqrt{-45} = 3\sqrt{5}i \).

Now we can substitute this back into the expression:

\[ 75 - \sqrt{-45} = 75 - 3\sqrt{5}i. \]

The result is:

\[ \text{The difference is } 75 - 3\sqrt{5}i. \]