Find the value of `sqrt80+3sqrt245-sqrt125`.

Answer

To solve the expression \( \sqrt{80} + 3\sqrt{245} - \sqrt{125} \), we will simplify each square root term step by step.

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

1. **Prime Factorization**:
\[ 80 = 16 \times 5 = 4^2 \times 5 \]
2. **Square Root**:
\[ \sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5} \]

### Step 2: Simplify \( 3\sqrt{245} \)

1. **Prime Factorization**:
\[ 245 = 49 \times 5 = 7^2 \times 5 \]
2. **Square Root**:
\[ \sqrt{245} = \sqrt{49 \times 5} = \sqrt{49} \times \sqrt{5} = 7\sqrt{5} \]
3. **Multiply by 3**:
\[ 3\sqrt{245} = 3 \times 7\sqrt{5} = 21\sqrt{5} \]

### Step 3: Simplify \( \sqrt{125} \)

1. **Prime Factorization**:
\[ 125 = 25 \times 5 = 5^2 \times 5 \]
2. **Square Root**:
\[ \sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} = 5\sqrt{5} \]

### Step 4: Combine the Terms

Now we can substitute back into the original expression:
\[ \sqrt{80} + 3\sqrt{245} - \sqrt{125} = 4\sqrt{5} + 21\sqrt{5} - 5\sqrt{5} \]

### Step 5: Combine Like Terms

Combine the coefficients of \( \sqrt{5} \):
\[ (4 + 21 - 5)\sqrt{5} = 20\sqrt{5} \]

### Final Answer

Thus, the value of \( \sqrt{80} + 3\sqrt{245} - \sqrt{125} \) is:
\[ \boxed{20\sqrt{5}} \]