Subtract 75–√−45–√

Question

The difference is what?

Answer 1

To simplify the expression $75-\sqrt{-45}$, we first need to simplify $\sqrt{-45}$.

We know that:

$$\sqrt{-45}=\sqrt{45}\cdot \sqrt{-1}=\sqrt{45}i$$

Next, we can simplify $\sqrt{45}$:

$$\sqrt{45}=\sqrt{9\cdot 5}=\sqrt{9}\cdot \sqrt{5}=3\sqrt{5}$$

So,

$$\sqrt{-45}=3\sqrt{5}i$$

Now, we can substitute this back into the original expression:

$$75-\sqrt{-45}=75-3\sqrt{5}i$$

The difference is:

$$75-3\sqrt{5}i$$

This is the final answer in the form of a complex number, where the real part is 75 and the imaginary part is $-3\sqrt{5}$. Thus, the expression $75-\sqrt{-45}$ simplifies to:

$$75-3\sqrt{5}i$$