Lakshesh Verma Lakshesh Verma

Lecture 2 : Revisiting irrational numbers & Revisiting rational numbers and their decimal expansion

  • Real Numbers Assignments 1

     Prove that root 5 is irrational.

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  • Real Numbers Assignments 2

    Explain why ( 7 x 11 x 13) + 13 is a composite number. 

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  • Real Numbers Assignments 3

    Show that 3√2 is irrational.

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  • Real Numbers Assignments 4

    Explain why 7×6×5×4×3×2×1+5 is a composite number.

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  • Real Numbers Assignments 5

     

    The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form  , what can you say about the prime factor of q?

    (i) 43.123456789 (ii) 0.120120012000120000… (iii) 

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  • Real Numbers Assignments 6

     

    Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.

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  • Real Numbers Assignments 7

     

    Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:

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  • Real Numbers Assignments 8

    Prove that the following are irrationals:

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  • Real Numbers Assignments 9

     

    Prove that  is irrational.

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  • Real Numbers Assignments 10

     

    Prove that  is irrational.

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    • Description:-

    Lecture 2:
    Today, we will discuss last two topics, i.e; Revisiting irrational numbers & Revisiting rational numbers and their decimal expansion respectively of Chapter 1 Real Numbers
    Objectives:
    1. Basic concept about Rational & Irrational numbers.
    2. Concept of proving irrational number.
    3. Expressing numbers in the form of p/q. 
    Important Tip: 
    This lecture about the above said last two topics of the chapter focuses on rational & irrational number. Functions and basic operations performed on them. Have a clear focus on these topics as it help you in further studies also.
    Please go through the topic, their notes. Properly do the assignments, watch videos of the concerned topics. If you have any doubt about any topic/point please submit it in the discussion section... it will be answered as soon as possible.
    After all of this... when you feel confident about the particular topic/chapter then take the quiz. 

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