Ms. Terkper's Digital Classroom

Unit 1: Number (Review) — Math 10C

Prime factors • Rational vs. irrational • Number systems • Radicals & mixed radicals

Prime Factorization Rationality Tests Real Number System Radical Simplification Entire ↔ Mixed

What You Should Be Able To Do

  • Prime-factorize integers and use prime factors to find GCF/LCM.
  • Classify numbers in the real number system and justify rational vs. irrational.
  • Simplify radicals and convert between entire and mixed radical forms.
  • Explain why certain radicals/decimals are rational or irrational.
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Video Library

Prime Factorization

Tree method and exponent form.

Real Number System & Rationality

Sets within ℝ; rational vs. irrational.

Radicals & Mixed Radicals

Perfect squares, entire ↔ mixed.

Repeating Decimals → Fractions

From \(0.\overline{3}\) or \(1.2\overline{34}\) to \( \frac{p}{q}\).

Interactive Lab

Prime Factorization + Factor Tree + GCF/LCM

Number-System & Rationality Analyzer

Radical Simplifier (Square Roots)

Random Practice

Generate a quick set of practice problems (answers shown below each set).

Unit 1 Quizzes

Quiz 1: Prime Factors & Number System

Prime factors • Applications (GCF/LCM) • Rational vs. irrational • Number systems

Quiz 2: Radicals & Mixed Radicals

Simplify radicals • entire ↔ mixed • basic operations

Downloadable Review

Download PDF

Quick Practice Scratchpad

Try: factor \(840\); classify \(0\), \(-\dfrac{5}{2}\), \(\sqrt{45}\); simplify \(\sqrt{180}\) and convert to entire radical.