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: $$5\sqrt{3}-3i\sqrt{5}$$