Final answer:
To find the product of (7√6 ⋅ √3), simplify the square roots before multiplying. The simplified expression is 21√2.
Step-by-step explanation:
To find the product of (7√6 ⋅ √3), we can simplify the square roots before multiplying. √6 can be simplified to √(2•3), which is equal to √2 • √3. Therefore, the expression becomes (7•√2 • √3) • √3.
When multiplying square roots, we can combine the coefficients and the radicands separately. The coefficients in this case are 7 and √2, which gives us 7√2. The radicands are √3 and √3, which gives us (√3)^2, or 3.
Combining the simplified coefficients and radicands, we get 7√2 • 3, which equals 21√2. Therefore, the correct answer is (b) 21√2.