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 of 11)

Answer 1

To perform the operation $3\sqrt{5}\times 7\sqrt{11}$, we can multiply the coefficients (3 and 7) and the square roots together.

Here are the steps:

1. Multiply the coefficients: $$3\times 7=21$$

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

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

Since the denominator is not present in this expression and does not need to be rationalized, the final answer is: $$\boxed{{\displaystyle 21\sqrt{55}}}$$