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Class 10MathematicsReal NumbersIrrational numbersExpertLevel 15
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If (\sqrt{m}) is irrational and (r) is a non-zero rational number then what type is (\frac{\sqrt{m}}{r})?

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Answer and explanation

Correct answer: Always irrational

Step 1: Dividing by a non-zero rational number is the same as multiplying by its reciprocal. Step 2: An irrational number multiplied by a non-zero rational number remains irrational. Step 3: Convert division questions into multiplication for easier reasoning.

Related tags

DivisionIrrational NumbersPropertiesClass 10

Frequently asked questions

What is the correct answer to this question?

Always irrational

Why is this the correct answer?

Step 1: Dividing by a non-zero rational number is the same as multiplying by its reciprocal. Step 2: An irrational number multiplied by a non-zero rational number remains irrational. Step 3: Convert division questions into multiplication for easier reasoning.

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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10 more MCQs
  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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