Okay, let's see. I need to find t(g(16)). Hmm, let me break this down step by step. First, I remember that functions are composed when you have one function inside another. So here, t is a function of x, and it's defined as 3 minus g(x). But since we need t(g(16)), that means we first apply the function g to 16 and then plug that result into the function t.

Alright, let me start by finding g(16). Since g(x) is given as the square root of x, that should be straightforward. The square root of 16 is 4, right? Because 4 times 4 is 16. So g(16) = 4. That part seems simple enough.

Now, the next step is to find t of that result. Since t(x) is 3 minus g(x), but wait, when we're evaluating t at g(16), which is 4, we need to substitute x with 4 in the function t. Wait, but hold on. Let me make sure I'm interpreting this correctly. The function t is defined as t(x) = 3 - g(x). So when we substitute x with g(16), which is 4, we get t(4) = 3 - g(4). But g(4) is the square root of 4, which is 2. So then t(4) would be 3 - 2, which is 1. So the final answer should be 1.

Wait, let me double-check to make sure I didn't mix up the functions. The problem states t(x) = 3 - g(x), and g(x) = sqrt(x). So t is a function that takes an input x, subtracts the square root of x from 3. Therefore, when we evaluate t at g(16), which is 4, we substitute x with 4 in t's definition. That gives us 3 - g(4), which is 3 - 2, which is indeed 1. 

Alternatively, maybe there's another way to look at this. Let's consider composing the functions. The composition t(g(x)) would be t(g(x)) = 3 - g(g(x)). But since g(x) = sqrt(x), then g(g(x)) would be sqrt(sqrt(x)), which is the fourth root of x. But in this problem, we're evaluating t(g(16)), so substituting x with 16 in the composed function. Wait, but that's not necessary here. The problem is t(g(16)), which is the same as substituting x with 16 in g(x) first, then substituting that result into t(x). So that's two separate steps: first compute g(16), then plug that into t. 

Let me confirm once more. If t(x) = 3 - g(x), then t(g(16)) = 3 - g(g(16)). Wait, hold on! Is that correct? Because t(g(16)) is substituting x with g(16) in the function t. So t(g(16)) = 3 - g(g(16)). But g(16) is 4, so then t(g(16)) = 3 - g(4). Which is 3 - 2 = 1. So that's the same result. So whether I think of it as substituting x with g(16) in t(x), or composing t(g(x)) and then substituting 16, I get the same answer. 

Wait, but why did I initially think of two different approaches? Let me clarify. If I compose t(g(x)), that would be replacing x in t's formula with g(x). So t(g(x)) = 3 - g(g(x)). Then evaluating at x=16 gives t(g(16)) = 3 - g(g(16)) = 3 - g(4) = 3 - 2 = 1. So both methods lead to the same answer. Therefore, the answer is 1. 

I think that's solid. Let me check with another example to make sure my reasoning is correct. Suppose instead of 16, we had 25. Then g(25) would be 5, and t(5) would be 3 - sqrt(5) ≈ 3 - 2.236 ≈ 0.764. So that works. Therefore, the process is correct. 

Another check: if we had x = 1, then g(1) = 1, and t(1) = 3 - 1 = 2. That's correct. So applying the same logic, substituting the inner function first and then the outer one gives the right result. 

Therefore, I'm confident that t(g(16)) is 1.
Therefore, the answer is $\boxed{1}$.
</think>