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The number tt is irrational. Which statement about 3+t3 + t is true?\newlineChoices:\newline(A) 3+t3 + t is rational.\newline(B) 3+t3 + t is irrational.\newline(C) 3+t3 + t can be rational or irrational, depending on the value of tt.

Full solution

Q. The number tt is irrational. Which statement about 3+t3 + t is true?\newlineChoices:\newline(A) 3+t3 + t is rational.\newline(B) 3+t3 + t is irrational.\newline(C) 3+t3 + t can be rational or irrational, depending on the value of tt.
  1. Identify Number 33: Identify the nature of the number 33.33 is a rational number because it can be expressed as a fraction (31\frac{3}{1}).
  2. Consider Number tt: Consider the nature of the number tt. tt 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 and an irrational number is always irrational. This is because if it were rational, then subtracting the rational number from both sides would leave an irrational number equal to a rational number, which is a contradiction.
  4. Apply Rule: Apply this rule to the given problem.\newlineSince 33 is rational and tt is irrational, their sum 3+t3 + t must be irrational.

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