Step-by-step explanation:

1. √√3²:

To simplify this expression, we start by evaluating the innermost square root:

√3² = √(3 * 3) = √9 = 3

Next, we evaluate the outer square root:

√√3² = √3 = √(3 * 1) = √3

2. √√2'n':

Similarly, we evaluate the innermost square root first:

√2'n' = √(2 * n) = √(2n)

Next, we evaluate the outer square root:

√√2'n' = √(√(2n)) = (√(2n))^(1/2) = (2n)^(1/4)

3. √√9:

Evaluating the innermost square root:

√9 = 3

Next, we evaluate the outer square root:

√√9 = √3 = √(3 * 1) = √3

4. √√8n¹:

Evaluating the innermost square root:

√8n¹ = √(8 * n) = √(8n)

Next, we evaluate the outer square root:

√√8n¹ = √(√(8n)) = (√(8n))^(1/2) = (8n)^(1/4)

Putting it all together, the complete solution is:

I => [ √3 √(2n) √3 (8n)^(1/4) ]