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The number is rational. Which statement about is true?Choices:(A) is rational.(B) is irrational.(C) can be rational or irrational, depending on the value of .
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Q. The number is rational. Which statement about is true?Choices:(A) is rational.(B) is irrational.(C) can be rational or irrational, depending on the value of .
- Identify Number Nature: Identify the nature of the number . is a rational number because it can be expressed as the ratio of two integers ().
- Consider Number : Consider the nature of the number . Since is given as a rational number, it can also be expressed as the ratio of two integers (, where and are integers and is not zero).
- Analyze Sum of Rational Numbers: Analyze the sum of two rational numbers. The sum of two rational numbers is always rational. This is because adding two fractions (or integers) results in another fraction (or integer) which can be simplified if necessary.
- Apply Property to : Apply the property to .Since both and are rational, their sum must also be rational.
- Choose Correct Statement: Choose the correct statement from the given choices.Based on the previous steps, the correct statement about is that it is rational.
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