Real Number System Practice: Level 2
Difficulty: 🟡 Intermediate | Focus: Square Roots, Fractions, & Advanced Properties
Section 1: Advanced Classification
Determine if the following numbers are Rational or Irrational. Explain your reasoning.
1. The number √16
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Answer: Rational.
Reason: √16 simplifies to 4, which is a whole number and can be written as 4/1.
2. The number √20
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Answer: Irrational.
Reason: 20 is not a perfect square. Its decimal form is non-terminating and non-repeating.
3. The number 0.333… (repeating)
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Answer: Rational.
Reason: Any repeating decimal can be written as a fraction (in this case, 1/3).
Section 2: Applying Properties
4. Use the Distributive Property to simplify: 5(2x + 3)
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Answer: 10x + 15
Step: Multiply 5 by 2x, then multiply 5 by 3.
5. Identify the property: (3 + 4) + 2 = 3 + (4 + 2)
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Answer: Associative Property of Addition.
Note: The grouping changed, but the order stayed the same.