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The number v v is rational. Which statement about v14 v - \sqrt{14} is true?\newlineChoices:\newline(A) v14 v - \sqrt{14} is rational.\newline(B) v14 v - \sqrt{14} is irrational.\newline(C) v14 v - \sqrt{14} can be rational or irrational, depending on the value of v v .

Full solution

Q. The number v v is rational. Which statement about v14 v - \sqrt{14} is true?\newlineChoices:\newline(A) v14 v - \sqrt{14} is rational.\newline(B) v14 v - \sqrt{14} is irrational.\newline(C) v14 v - \sqrt{14} can be rational or irrational, depending on the value of v v .
  1. Identify Type of Number: Identify whether 14\sqrt{14} is a rational or irrational number.1414 is a non-perfect square.14\sqrt{14} is an irrational number.
  2. Properties of Numbers: Consider the properties of rational and irrational numbers. A rational number minus an irrational number is always irrational.
  3. Apply Property: Apply the property to the given problem.\newlineSince vv is rational and 14\sqrt{14} is irrational, v14v - \sqrt{14} must be irrational.

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