Verified answer

Answer:

D. When n is positive

Step-by-step explanation:

For there to be only one real nth root of Va, the expression Va must be non-negative (or zero). This is because the nth root of a negative number is not real for even values of n.

So, we have:

Va ≥ 0

a^n/2 ≥ 0

This is true for all values of a and n, as long as n is a positive number.

Therefore, the answer is D. When n is positive.

Answer:

Only if VA = odd positive integer

Step-by-step explanation:

In the expression Va, if a is a positive number, there will be only one real nth root if and only if n is an odd positive integer.

If n is even, then there will be two nth roots of a, one positive and one negative.

If n is negative, then the expression V(a) raised to the power 1/n is undefined because taking an even root of a positive number gives a positive result, and taking an odd root of a negative number gives a negative result.

If n is odd, then there will be only one nth root of a, which will be a positive real number.

Therefore, the only condition where there will be only one real nth root in the expression Va is when n is an odd positive integer.