Final answer:
The expression √5⋅√7+2√35 simplifies to 3√35 by recognizing that √5⋅√7 is √35 and combining like terms to add 1√35 to 2√35. The answer choices provided do not include this solution.
Step-by-step explanation:
The student has asked us to simplify the expression √5⋅√7+2√35. To solve this, we need to understand the properties of square roots and how to combine them. The square root of a product, based on the property √x² = x, is equivalent to the product of the square roots of each factor. In this case, √5⋅√7 is equivalent to √(5⋇5), and since 5⋇5 = 35, we have √35. Therefore, √5⋅√7 simplifies to √35.
Now, the expression √5⋅√7+2√35 becomes √35+2√35. Since we have like terms, we can add them together. Think of √35 as 1√35, so when we add 1√35 to 2√35, we get 3√35. None of the answer choices matches this result, so it appears there might have been a mistake in the options provided. If we make sure to repeatedly check that our solution is reasonable, we'll avoid mistakes and ensure accuracy.