h' = \sqrt100 - \frac(8+4)^24 = \sqrt100 - 36 = \sqrt64 = 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.

Understanding the Context

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.

$h' = \sqrt{100 - \frac{(8+4)^2}{4}} = \sqrt{100 - 36} = \sqrt{64} = 8$

Key Insights

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

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Final Thoughts

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