`2sqrt(2)xx3sqrt(3)xx5sqrt(2)xx9sqrt(3)=?`

Options

A. 1874
B. 1340
C. 1620
D. 2140

Explanation

To solve the expression \( 2\sqrt{2} \times 3\sqrt{3} \times 5\sqrt{2} \times 9\sqrt{3} \), we can follow these steps:

### Step 1: Group the terms
We can group the terms with the same square roots together:
\[ (2\sqrt{2} \times 5\sqrt{2}) \times (3\sqrt{3} \times 9\sqrt{3}) \]

### Step 2: Simplify each group
Now, let's simplify each group separately.

**For the first group:**
\[ 2\sqrt{2} \times 5\sqrt{2} = (2 \times 5)(\sqrt{2} \times \sqrt{2}) = 10 \times 2 = 20 \]

**For the second group:**
\[ 3\sqrt{3} \times 9\sqrt{3} = (3 \times 9)(\sqrt{3} \times \sqrt{3}) = 27 \times 3 = 81 \]

### Step 3: Multiply the results of the groups
Now we multiply the results from both groups:
\[ 20 \times 81 \]

### Step 4: Calculate the final result
Calculating \( 20 \times 81 \):
\[ 20 \times 81 = 1620 \]

Thus, the final answer is:
\[ \boxed{1620} \]