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Class 10MathematicsReal NumbersIrrational numbersExpertLevel 15
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Which option gives the correct general conclusion for the difference of a rational and an irrational number?

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Answer and explanation

Correct answer: Always irrational

Step 1: Let (r) be rational and (s) be irrational. Step 2: If (r-s) were rational then (s=r-(r-s)) would be rational which is false. Step 3: Adding or subtracting a rational and an irrational number gives an irrational number.

Related tags

PropertiesIrrational NumbersProofClass 10

Frequently asked questions

What is the correct answer to this question?

Always irrational

Why is this the correct answer?

Step 1: Let (r) be rational and (s) be irrational. Step 2: If (r-s) were rational then (s=r-(r-s)) would be rational which is false. Step 3: Adding or subtracting a rational and an irrational number gives an irrational number.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Irrational numbers.

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  1. 1Which of the following numbers is irrational?
  2. 2Which of the following numbers is rational?
  3. 3What type of number is (\sqrt{16})?
  4. 4Which statement about (\sqrt{10}) is correct?
  5. 5Which of the following is an example of an irrational number?
  6. 6Which decimal form represents an irrational number?
  7. 7What type of number is (0.3333\ldots)?
  8. 8Which statement is correct about (0.101001000100001\ldots)?
  9. 9If (a) is a non-zero rational number and (b) is an irrational number, what type of number is (ab) generally?
  10. 10What type of number is (\sqrt{2}+3)?
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