`sqrt(10).sqrt(15)` is equal to

Options

A. `6sqrt(5)`
B. `5sqrt(6)`
C. `sqrt(25)`
D. `10sqrt(5)`

Explanation

To solve the expression \( \sqrt{10} \cdot \sqrt{15} \), we can follow these steps:

### Step 1: Rewrite the square roots
We can express \( \sqrt{10} \) and \( \sqrt{15} \) in terms of their prime factors:
\[ \sqrt{10} = \sqrt{2 \cdot 5} \]
\[ \sqrt{15} = \sqrt{3 \cdot 5} \]

### Step 2: Multiply the square roots
Using the property of square roots that states \( \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} \), we can combine the two square roots:
\[ \sqrt{10} \cdot \sqrt{15} = \sqrt{10 \cdot 15} \]

### Step 3: Calculate the product inside the square root
Now, we calculate \( 10 \cdot 15 \):
\[ 10 \cdot 15 = 150 \]
Thus, we have:
\[ \sqrt{10} \cdot \sqrt{15} = \sqrt{150} \]

### Step 4: Simplify \( \sqrt{150} \)
Next, we simplify \( \sqrt{150} \) by factoring it:
\[ 150 = 25 \cdot 6 \]
So,
\[ \sqrt{150} = \sqrt{25 \cdot 6} = \sqrt{25} \cdot \sqrt{6} \]
Since \( \sqrt{25} = 5 \), we get:
\[ \sqrt{150} = 5 \cdot \sqrt{6} \]

### Final Result
Thus, the final result is:
\[ \sqrt{10} \cdot \sqrt{15} = 5\sqrt{6} \]