By how much does `5sqrt(7)-2sqrt(5)` exceed `3sqrt(7)-4sqrt(5)` ?

Options

A. `5(sqrt(7)+sqrt(5))`
B. `sqrt(7)+sqrt(5)`
C. `2(sqrt(7)+sqrt(5))`
D. `7(sqrt(2)+sqrt(5))`

Answer

To find out by how much \( 5\sqrt{7} - 2\sqrt{5} \) exceeds \( 3\sqrt{7} - 4\sqrt{5} \), we need to calculate the difference between the two expressions. Here’s how to do it step by step:

### Step 1: Write down the expressions
We have two expressions:
1. \( A = 5\sqrt{7} - 2\sqrt{5} \)
2. \( B = 3\sqrt{7} - 4\sqrt{5} \)

### Step 2: Set up the difference
We need to find \( A - B \):
\[ A - B = (5\sqrt{7} - 2\sqrt{5}) - (3\sqrt{7} - 4\sqrt{5}) \]

### Step 3: Distribute the negative sign
Distributing the negative sign in the second expression gives:
\[ A - B = 5\sqrt{7} - 2\sqrt{5} - 3\sqrt{7} + 4\sqrt{5} \]

### Step 4: Combine like terms
Now, we can combine the like terms:
- For \( \sqrt{7} \) terms: \( 5\sqrt{7} - 3\sqrt{7} = 2\sqrt{7} \)
- For \( \sqrt{5} \) terms: \( -2\sqrt{5} + 4\sqrt{5} = 2\sqrt{5} \)

Thus, we have:
\[ A - B = 2\sqrt{7} + 2\sqrt{5} \]

### Step 5: Factor out the common factor
We can factor out the common factor of 2:
\[ A - B = 2(\sqrt{7} + \sqrt{5}) \]

### Final Answer
The expression \( 5\sqrt{7} - 2\sqrt{5} \) exceeds \( 3\sqrt{7} - 4\sqrt{5} \) by:
\[ 2(\sqrt{7} + \sqrt{5}) \]

---