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The number yy is irrational. Which statement about 28y\sqrt{28} - y is true?\newlineChoices:\newline(A) 28y\sqrt{28} - y is rational.\newline(B) 28y\sqrt{28} - y is irrational.\newline(C) 28y\sqrt{28} - y can be rational or irrational, depending on the value of yy.

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Q. The number yy is irrational. Which statement about 28y\sqrt{28} - y is true?\newlineChoices:\newline(A) 28y\sqrt{28} - y is rational.\newline(B) 28y\sqrt{28} - y is irrational.\newline(C) 28y\sqrt{28} - y can be rational or irrational, depending on the value of yy.
  1. Identify Type of Number: Identify whether 28\sqrt{28} is a rational or irrational number. 2828 is a non-perfect square, which means that its square root cannot be expressed as a ratio of two integers. 28\sqrt{28} is an irrational number.
  2. Properties of Irrational Numbers: Consider the properties of irrational numbers. The difference between two irrational numbers can be rational or irrational. For example, if y=28y = \sqrt{28}, then 2828=0\sqrt{28} - \sqrt{28} = 0, which is rational. However, if yy is any other irrational number, then 28y\sqrt{28} - y is likely to be irrational.
  3. Describe 28y\sqrt{28} - y: Determine the statement that correctly describes 28y\sqrt{28} - y. Since we have shown that 28y\sqrt{28} - y can be rational (if y=28y = \sqrt{28}) or irrational (if yy is any other irrational number), the correct statement is that 28y\sqrt{28} - y can be rational or irrational, depending on the value of yy.

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