h' = \sqrt{100 - \frac(8+4)^24} = \sqrt100 - 36 = \sqrt64 = 8 - Blask
Understanding the Simplified Equation: h = √(100 − ((8 + 4)²)/4) = 8 – A Step-by-Step Breakdown
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.
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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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
