h' = \sqrt{100 - \frac{(8+4)^2}{4}} = \sqrt{100 - 36} = \sqrt{64} = 8
Understanding the Simplified Equation: h = √(100 − ((8 + 4)²)/4) = 8 – A Step-by-Step Breakdown
Mathematics often appears complex, but many problems can be simplified using clear logical steps. Today, we explore the elegant solution: h = √[100 − ( (8 + 4)² ) / 4 ] = √(64) = 8
In this article, we’ll walk through the calculation step-by-step, explain the logic behind each transformation, and highlight how breaking down expressions enhances understanding and retention — fundamental skills for mastering algebra and problem-solving.
Step-by-Step Explanation of the Equation
1. Start with the Original Expression
We begin with: h = √[100 − ( (8 + 4)² ) / 4 ]
The goal is to simplify inside the square root to reveal the value of h.
2. Simplify the Parentheses
The expression inside the large parentheses begins with addition: (8 + 4) = 12
So now the equation becomes: h = √[100 − (12²) / 4]
3. Square the Result
Calculate 12 squared: 12² = 144
Now update the expression: h = √[100 − (144 / 4)]
4. Perform Division Inside Parentheses
Divide 144 by 4: 144 ÷ 4 = 36
The equation now simplifies to: h = √(100 − 36)
5. Subtract Inside the Square Root
Subtract inside the radical: 100 − 36 = 64
Resulting in: h = √64
6. Evaluate the Square Root
The square root of 64 is a standard value: √64 = 8
Thus, h = 8
Why This Process Matters
At first glance, nested operations like fractions within parentheses and square roots may seem intimidating. But by isolating each step, we reveal that:
- Order of operations matters: Always simplify inside the parentheses first.
- Distribution and simplification reduce work step-by-step.
- Recognizing perfect squares (like √64 = 8) accelerates the solution.
This method is not only useful for solving this specific equation but also builds a solid foundation for tackling broader algebraic concepts — from quadratic expressions to functions and beyond.
Practical Applications and Next Steps
Understanding how to simplify such expressions helps in various fields:
- Physics: Calculating distances, velocities, and resolving forces.
- Engineering: Designing structures and systems requiring precise measurements.
- Data Science: Interpreting formulas in statistical models.
Want to reinforce your skills? Practice similar problems with different numbers, and try articulating each step aloud or in writing. This reinforces memory and deepens comprehension through active learning.
Final Takeaway The path from h = √[100 − ( (8 + 4)² ) / 4] to h = 8 illustrates how systematic simplification turns complexity into clarity. Mastering such procedures empowers you to solve more advanced mathematical challenges with confidence.
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Meta Description: Solve h = √[100 − ((8 + 4)²)/4] easily with a clear step-by-step breakdown — from parentheses to square root, learn how to simplify complex algebraic expressions confidently.
