Certainly! Let's work through the problem step-by-step.
We need to evaluate the expression \(\sqrt{10} \times \sqrt{15}\).
Step 1: Use the property of square roots:
[tex]\[ \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} \][/tex]
Applying this property to our expression:
[tex]\[ \sqrt{10} \times \sqrt{15} = \sqrt{10 \times 15} \][/tex]
Step 2: Compute the product inside the square root:
[tex]\[ \sqrt{10 \times 15} = \sqrt{150} \][/tex]
Step 3: Simplify \(\sqrt{150}\). We can factor 150 into its prime factors:
[tex]\[ 150 = 25 \times 6 = 5^2 \times 6 \][/tex]
Step 4: Extract the square root of the perfect square:
[tex]\[ \sqrt{150} = \sqrt{5^2 \times 6} \][/tex]
[tex]\[ \sqrt{150} = 5 \times \sqrt{6} \][/tex]
Therefore:
[tex]\[ \sqrt{10} \times \sqrt{15} = 5 \sqrt{6} \][/tex]
Thus, the correct answer is [tex]\(\boxed{5 \sqrt{6}}\)[/tex], which corresponds to option (B).
