Simplify. $$ \sqrt{125}+\sqrt{28}-8 \sqrt{5} $$ $$ [?] \sqrt{\square}-\square \sqrt{\square} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\sqrt{125} + \sqrt{28} - 8 \sqrt{5}
$$

Let's break it down step by step.

1. **Simplify each square root:**
   - $$\sqrt{125} = \sqrt{25 \times 5} = 5\sqrt{5}$$
   - $$\sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7}$$

2. **Substitute the simplified forms back into the expression:**

$$
5\sqrt{5} + 2\sqrt{7} - 8\sqrt{5}
$$

3. **Combine like terms:**
   - Combine the terms with $$\sqrt{5}$$:
   
$$
5\sqrt{5} - 8\sqrt{5} = -3\sqrt{5}
$$

- The term with $$\sqrt{7}$$ remains as is:
   
$$
2\sqrt{7}
$$

4. **Write the final simplified expression:**

$$
2\sqrt{7} - 3\sqrt{5}
$$

So, the expression in the desired format is:

$$
\boxed{2\,\sqrt{7}\ -\ 3\,\sqrt{5}}
$$
$$ 2\sqrt{7} - 3\sqrt{5} $$

Simplify.