To solve the equation \(74 + 7 - h^2 = 0\) and find the value of \(\frac{1}{3}h\), we can follow these steps:

### Step 1: Simplify the Equation
First, let's simplify the given equation:
\[
74 + 7 - h^2 = 0
\]

Combine like terms:
\[
81 - h^2 = 0
\]

### Step 2: Solve for \(h^2\)
Rearrange the equation to isolate \(h^2\):
\[
h^2 = 81
\]

### Step 3: Solve for \(h\)
Take the square root of both sides:
\[
h = \sqrt{81} \quad \text{or} \quad h = -\sqrt{81}
\]

Since \(\sqrt{81} = 9\), we have:
\[
h = 9 \quad \text{or} \quad h = -9
\]

### Step 4: Find the Value of \(\frac{1}{3}h\)
Now, calculate \(\frac{1}{3}h\) for both values of \(h\):

1. If \(h = 9\):
   \[
   \frac{1}{3}h = \frac{1}{3} \times 9 = 3
   \]

2. If \(h = -9\):
   \[
   \frac{1}{3}h = \frac{1}{3} \times (-9) = -3
   \]

### Conclusion
The value of \(\frac{1}{3}h\) can be either \(3\) or \(-3\), depending on whether \(h = 9\) or \(h = -9\).

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Would you like further details on any step, or do you have any other questions?  

Here are 5 related questions that you might find interesting:
1. What are the properties of quadratic equations?
2. How do you solve equations involving square roots?
3. How can you determine if an equation has real or complex solutions?
4. What is the significance of absolute values when dealing with square roots?
5. How does factoring help in solving quadratic equations?

**Tip:** Remember that taking the square root of a number yields both a positive and a negative solution.

Learn how to solve the equation 74 + 7 - h^2 = 0 and find the value of 1/3h with a step-by-step solution. This problem covers algebraic concepts and quadratic equation solving. Suitable for students in Grades 7-9.

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