Add and Subtract Radicals Practice

Question

Complete this assessment to review what you've learned. It will not count toward your grade.
3 of 53 of 5 Items
Question
Subtract 75–√−45–√
.(1 point)
The difference is
.

Answer 1

To subtract the square roots \( \sqrt{75} - \sqrt{-45} \), we first simplify the radicals.

1. Simplify \( \sqrt{75} \):
   \[ \sqrt{75} = \sqrt{25 \cdot 3} = \sqrt{25} \cdot \sqrt{3} = 5\sqrt{3} \]

2. Simplify \( \sqrt{-45} \):
   \[ \sqrt{-45} = \sqrt{-1 \cdot 45} = \sqrt{-1} \cdot \sqrt{45} = i \sqrt{45} \] Now simplify \( \sqrt{45} \): \[ \sqrt{45} = \sqrt{9 \cdot 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5} \] Thus,
   \[ \sqrt{-45} = i \cdot 3\sqrt{5} = 3i\sqrt{5} \]

3. Substituting back into the expression:
   Now we can rewrite the expression: \[ \sqrt{75} - \sqrt{-45} = 5\sqrt{3} - 3i\sqrt{5} \]

The difference is: \[ 5\sqrt{3} - 3i\sqrt{5} \]