Perform the indicated operation be sure to rationalize the denominator when necessary make sure to simply as much as possible and give the exact answer

Question

3(square root of 5) times 7(square root of11)

Answer 1

To perform the operation $3\sqrt{5}\times 7\sqrt{11}$, we can follow these steps:

1. Multiply the coefficients (the numbers outside the square roots): $$3\times 7=21.$$

2. Multiply the square roots together: $$\sqrt{5}\times \sqrt{11}=\sqrt{5\times 11}=\sqrt{55}.$$

3. Combine the results: $$3\sqrt{5}\times 7\sqrt{11}=21\sqrt{55}.$$

Since $\sqrt{55}$ is already in its simplest form and there is no need to rationalize the denominator here (as there is no denominator), the final answer is: $$\boxed{{\displaystyle 21\sqrt{55}}}.$$