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The number zz is irrational. Which statement about 9+z9 + z is true?\newlineChoices:\newline(A) 9+z9 + z is rational.\newline(B) 9+z9 + z is irrational.\newline(C) 9+z9 + z can be rational or irrational, depending on the value of zz.

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Full solution

Q. The number zz is irrational. Which statement about 9+z9 + z is true?\newlineChoices:\newline(A) 9+z9 + z is rational.\newline(B) 9+z9 + z is irrational.\newline(C) 9+z9 + z can be rational or irrational, depending on the value of zz.
  1. Identify Number 99: Identify the nature of the number 99.99 is a rational number because it can be expressed as a fraction (91\frac{9}{1}).
  2. Understand Number zz: Understand the nature of the number zz.zz is given as an irrational number, which means it cannot be expressed as a fraction of two integers.
  3. Analyze Sum: Analyze the sum of a rational and an irrational number.\newlineThe sum of a rational number 99 and an irrational number zz is always irrational. This is because if the sum were rational, then subtracting the rational part 99 from it would leave us with a rational number, which contradicts the fact that zz is irrational.
  4. Conclude Result: Conclude the nature of 9+z9 + z. Since adding a rational number to an irrational number results in an irrational number, 9+z9 + z is irrational.

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