NCERT Class 9 Solutions: Number Systems (Chapter 1) Exercise 1.5 – Part 1

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Q-1 Classify the following numbers as rational or irrational:

  1. 25

  2. (3+23)23

  3. 2777

  4. 12

  5. 2π

Solution:

Classifying rational and irrational numbers

Rational vs Irrational Numbers

Classifying rational and irrational numbers

  • Given multiple numbers and classify the numbers as rational or irrational

  1. 25=22.2360679=0.2360679..

    Since it is non-terminating and non-recurring number

    So, it is an irrational number

  2. (3+23)23=3+2323=3=31

    Since the number can be written pq form

    So, it is a rational number

  3. 2777=27

    Since the number can be written pq form

    So, it is a rational number

  4. 12=1×22×2=22=1.4142135623.2=0.707106

    Since it is non-terminating and non-recurring number

    So, it is an irrational number

  5. 2π=2×3.141528.=6.283056.

    Since it is non-terminating and non-recurring number

    So, it is an irrational number

Q-2 Simplify each of the following expressions:

  1. (3+3)(2+2)

  2. (3+3)(33)

  3. (5+2)2

  4. (52)(5+2)

Solution:

  1. (3+3)(2+2)=3×2+32+23+3×2 = 6+32+23+6

  2. (3+3)(33)

    Using identify (a+b)(ab)=a2b2

    (3+3)(33)=323=93=6

  3. (5+2)2

    Using identify (a+b)2=a2+b2+2ab

    (5+2)2=5+2+252=7+210

  4. (52)(5+2)

    Using identify (a+b)(a