How much greater `5sqrt7-2sqrt5` from `3sqrt7 -4sqrt5`?

Options

A. `5(sqrt7+sqrt5)`
B. `sqrt7+sqrt5`
C. `2(sqrt7+sqrt5)`
D. `7(sqrt2+sqrt5)`

Answer

To find out how much greater \( 5\sqrt{7} - 2\sqrt{5} \) is from \( 3\sqrt{7} - 4\sqrt{5} \), we will subtract the second expression from the first one. Here are the steps:

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

### Step 2: Set up the subtraction
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 gives us:
\[ A - B = 5\sqrt{7} - 2\sqrt{5} - 3\sqrt{7} + 4\sqrt{5} \]

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

### Step 5: Write the final expression
Putting it all together, we have:
\[ A - B = 2\sqrt{7} + 2\sqrt{5} \]

### Step 6: Factor out the common term
We can factor out the common factor of 2:
\[ A - B = 2(\sqrt{7} + \sqrt{5}) \]

### Final Answer
Thus, \( 5\sqrt{7} - 2\sqrt{5} \) is \( 2(\sqrt{7} + \sqrt{5}) \) greater than \( 3\sqrt{7} - 4\sqrt{5} \).

---