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8th Class Mathematics Rational Numbers Question Bank Numbers

  • question_answer
    DIRECTIONS: Following questions consist of two statements, one labelled as the ?Assertion (A)? and the other as ?Reason (R)?. You are to examine these two statements carefully and select the answer to these items using the code given below. Assertion: \[5\sqrt{3}\] is an irrational number.                  Reason: For any two given integers a and b there exist unique integers q and r satisfying \[a=bq+r.0\le r<b\]

    A) Both A and R are individually true and R is the correct explanation of A.

    B) Both A and R are individually true but R is not the correct explanation of.

    C) A is true but R is false

    D) A is false but R is true.

    Correct Answer: B

    Solution :

    If possible, let \[5\sqrt{3}\] be a rational number. So \[5\sqrt{3}=\frac{p}{q},\] where p and q are integers and \[q\ne 0\] \[\Rightarrow \]  \[\sqrt{3}=\frac{p}{5q}\] Since, p, q and 5 are integers therefore \[\frac{p}{5q}\] is a rational umber. Hence,  \[\sqrt{3}\] is a rational number, which is a contradiction. Therefore, \[5\sqrt{3}\] is an irrational number. \[\therefore \] Assertion is true. Reason is also true but not the correct explanation of Assertion.


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