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)
To prove that the product of 2π and 3/4 is an irrational number, we need to show that it cannot be expressed as a fraction p/q, where p and q are integers. The product is 2π * 3/4 = 3π/2. Since π is an irrational number, and any non-zero rational number multiplied by an irrational number is still irrational, we can conclude that 3π/2 is also an irrational number.
To prove that the product of 2π and 3/4 is an irrational number, we first need to find the product. The product of 2π and 3/4 is (2π) * (3/4) = 6π/4 = 3π/2. To explain why this value is irrational, we need to show that it cannot be expressed as a fraction of two integers where the denominator is not zero. However, since π is an irrational number, any multiple of π (such as 3π/2) will also be irrational, and hence the product 3π/2 is also irrational.
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.
