Math Problem Statement

Simplify (12 - 3/5 * √25)² + (2 - 4)²

Solution

The extracted text from the image is not fully accurate, but from observation, the equation seems to be:

(123525)2+(24)2\left( 12 - \frac{3}{5} \cdot \sqrt{25} \right)^2 + (2 - 4)^2

Let's break it down step by step.

First Expression:

12352512 - \frac{3}{5} \cdot \sqrt{25}

  • 25=5\sqrt{25} = 5
  • So the expression becomes: 12355=123=912 - \frac{3}{5} \cdot 5 = 12 - 3 = 9 Now square it: 92=819^2 = 81

Second Expression:

(24)2=(2)2=4(2 - 4)^2 = (-2)^2 = 4

Final Calculation:

81+4=8581 + 4 = 85

Thus, the simplified expression evaluates to 85.

Would you like further explanation, or do you have any other questions? Here are five related questions you might consider:

  1. How do you simplify expressions with roots and fractions?
  2. What are the properties of squaring negative numbers?
  3. How does the order of operations affect the outcome of this problem?
  4. How do you evaluate complex expressions step by step?
  5. What strategies can you use to avoid common mistakes when simplifying?

Tip: Always simplify any square roots and perform operations inside parentheses before applying exponents.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplifying Expressions
Exponents

Formulas

(a - b)^2
√x = square root of x

Theorems

Exponentiation
Order of Operations

Suitable Grade Level

Grades 6-8