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The number yy is irrational. Which statement about y9y - 9 is true?\newlineChoices:\newline(A)y9y - 9 is rational.\newline(B)y9y - 9 is irrational.\newline(C)y9y - 9 can be rational or irrational, depending on the value of yy.

Full solution

Q. The number yy is irrational. Which statement about y9y - 9 is true?\newlineChoices:\newline(A)y9y - 9 is rational.\newline(B)y9y - 9 is irrational.\newline(C)y9y - 9 can be rational or irrational, depending on the value of yy.
  1. Identify Number 99: Identify the nature of the number 99. 99 is a perfect square and its square root is 33. Therefore, 99 is a rational number.
  2. Subtract Rational from Irrational: Consider the subtraction of a rational number from an irrational number. Subtracting a rational number from an irrational number will result in an irrational number. This is because the difference between a rational and an irrational number cannot be expressed as a ratio of two integers.
  3. Apply Rule to Problem: Apply this rule to the given problem.\newlineSince yy is irrational and 99 is rational, y9y - 9 will be irrational.

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