https://file.aiquickdraw.com/mathbot/file/1725427700092uc64in74.jpg

The expression you provided is:

\[
\sqrt{80} + \sqrt{125}
\]

To simplify this, let's first simplify each square root term separately.

### Step 1: Simplify \(\sqrt{80}\)

\[
\sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5}
\]

### Step 2: Simplify \(\sqrt{125}\)

\[
\sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} = 5\sqrt{5}
\]

### Step 3: Combine the simplified terms

Now, substitute the simplified forms back into the expression:

\[
4\sqrt{5} + 5\sqrt{5}
\]

Since both terms have the common factor \(\sqrt{5}\), we can combine them:

\[
(4 + 5) \sqrt{5} = 9\sqrt{5}
\]

### Final Answer

\[
\sqrt{80} + \sqrt{125} = 9\sqrt{5}
\]

Would you like more details, or do you have any other questions? Here are some related questions that might interest you:

1. How do you simplify expressions involving cube roots?
2. What are some techniques to simplify radicals with larger numbers?
3. How do you add or subtract square roots with different radicands?
4. What are the rules for multiplying and dividing square roots?
5. Can you explain how to rationalize a denominator?

**Tip:** Remember that combining like terms, including those involving radicals, requires the same factor (like \(\sqrt{5}\) in this case).

Simplify the expression \(\sqrt{80} + \sqrt{125}\).

Learn how to simplify the expression \(\sqrt{80} + \sqrt{125}\) by breaking down the square roots and combining like terms. This step-by-step solution involves the simplification of radicals, making it suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation