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The image contains a series of exercises for a math homework assignment, covering topics in algebra, radicals, simplification, and scientific notation. I’ll provide a breakdown for each exercise and solve the questions systematically.

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### Exercise 1
1. **Calculate** values of expressions involving square roots and basic arithmetic.
   - \( A = \sqrt{64} + \sqrt{(−3)^2} \)
   - \( B = \sqrt{45} \times \sqrt{2} + \sqrt{432} \)
   - etc.

2. **Rewrite expressions** in the form \( a\sqrt{b} \) where \( a \) and \( b \) are integers.

3. **Rationalize denominators** in given expressions.

4. **Show that** \( F \) is an integer for a given expression with square roots.

5. **Solve equations** involving square roots and polynomial expressions.

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### Exercise 2
1. **Expand and simplify** expressions like \( (2x + 1)^2 \).

2. **Factorize** given polynomials.

3. **Verify** an equation involving radicals.

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### Exercise 3
1. **Calculate** values involving exponents and roots.

2. **Rewrite as a single power** given a set of expressions.

3. **Write in scientific notation** for numerical expressions.

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Would you like me to solve specific questions from each exercise or go through all the problems in detail? 

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Here are five follow-up questions related to the content:

1. How do you simplify expressions involving square roots?
2. What steps are required to rationalize a denominator?
3. How do you verify if an expression with roots is an integer?
4. What are the key techniques for expanding binomials?
5. How can you convert between standard and scientific notation?

**Tip:** When simplifying expressions with radicals, look for perfect squares that can be extracted from under the square root.

A math homework assignment covering topics in algebra, radicals, simplification, factorization, and scientific notation, with various exercises to calculate values, rewrite expressions, rationalize denominators, verify integer properties, solve equations, expand and simplify binomials, factorize polynomials, and use scientific notation.

Solve a comprehensive math homework covering algebraic simplifications, radicals, rationalization, scientific notation, factorization, and equation solving. This worksheet includes step-by-step exercises for expanding expressions, rationalizing denominators, verifying integer values, and using scientific notation.

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