Question

Examine the reasoning in the first two explorations. Can you apply the same reasoning for any nth root, √a, where n is a natural number? Explain. What can you conclude?

a) Yes, the same reasoning can be applied, and the conclusion is that the nth root of a is always a real number.
b) No, the reasoning does not apply to all nth roots, and the conclusion is that some nth roots are not real numbers.
c) Yes, the same reasoning can be applied, and the conclusion is that the nth root of a is always an imaginary number.
d) No, the reasoning does not apply to all nth roots, and the conclusion is that some nth roots may be real or imaginary.

Answer 1

The same reasoning can be applied for any nth root, where n is a natural number, and the conclusion is that the nth root of a is always a real number.

Step-by-step explanation:

The reasoning in the first two explorations involves taking the square root of a number. For example, to find the square root of 5, we square 5 which gives us 25. So, the square root of 25 is 5. The same reasoning can be applied to any nth root, where n is a natural number. For instance, the cube root of 8 is 2 because when we cube 2, we get 8. Therefore, the conclusion is that the nth root of a is always a real number, which means option a is correct.