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Synthesize prime factorization theorems and proofs of irrationality across varying problem contexts.
Review checklist of chapter outcomes.
Progressive difficulty MCQs spanning the chapter.
What is the LCM of two numbers if their prime factorizations are 2² × 3¹ × 5¹ and 2¹ × 3²?
Exercise 1.2 Q3(iii) 6 + sqrt(2).
Use the method of contradiction. Assume is rational, meaning it can be written as where and are coprime integers (). Rearrange the equation to isolate the irrational component, and explain why this creates a logical contradiction.
Write down the final rearranged equation that isolates the square root on one side.
Explain in words why your final equation presents a mathematical impossibility.
State the general rule demonstrated by this proof.