`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 use the property of square roots that states \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\).

### Step-by-step solution:

1. **Combine the square roots**:
\[ \sqrt{10} \cdot \sqrt{15} = \sqrt{10 \cdot 15} \]

2. **Calculate the product inside the square root**:
\[ 10 \cdot 15 = 150 \]
So, we have:
\[ \sqrt{10 \cdot 15} = \sqrt{150} \]

3. **Simplify \(\sqrt{150}\)**:
To simplify \(\sqrt{150}\), we can factor 150 into its prime factors:
\[ 150 = 2 \cdot 3 \cdot 5^2 \]
Therefore:
\[ \sqrt{150} = \sqrt{2 \cdot 3 \cdot 5^2} \]

4. **Apply the square root property**:
Using the property \(\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}\), we can separate the square root:
\[ \sqrt{150} = \sqrt{2} \cdot \sqrt{3} \cdot \sqrt{5^2} \]
Since \(\sqrt{5^2} = 5\), we have:
\[ \sqrt{150} = 5 \cdot \sqrt{2 \cdot 3} = 5 \cdot \sqrt{6} \]

5. **Final result**:
Therefore, the expression \(\sqrt{10} \cdot \sqrt{15}\) simplifies to:
\[ \sqrt{10} \cdot \sqrt{15} = 5\sqrt{6} \]

### Final Answer:
\[ \sqrt{10} \cdot \sqrt{15} = 5\sqrt{6} \]