Prove that the product of 2π and 3/4 is an irrational number. Find the product and explain why the value is irrational. Explain your reasoning in 1–2 sentences.(2 points)
3 answers
The product of 2π and 3/4 is (2π)(3/4) = (6π)/4 = (3π)/2. To prove it is irrational, we need to show that it cannot be expressed as a fraction (ratio) of two integers. Since π is irrational and 3/2 is a fraction, (3π)/2 cannot be expressed as a ratio of two integers, making it irrational.
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