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Classify the following numbers as rational or irrational according to their type: (i)√23 (ii)√225 (iii) 0.3796 (iv) 7.478478 (v) 1.10100100010000 . Q.9

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In chapter number system of ncert class 9th what is the best solution of the question exercise 1.3 question number 9 . Find the best and easiest way to solve the question , Sir please help me to solve the best solution of the question number 9.Classify the following numbers as rational or irrational according to their type: (i)√23 (ii)√225 (iii) 0.3796 (iv) 7.478478 (v) 1.10100100010000 .

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  1. (i)√23

    Solution:

    √23 = 4.79583152331…

    Since the number is non-terminating non-recurring therefore, it is an irrational number.

    (ii)√225

    Solution:

    √225 = 15 = 15/1

    Since the number can be represented in p/q form, it is a rational number.

    (iii) 0.3796

    Solution:

    Since the number,0.3796, is terminating, it is a rational number.

    (iv) 7.478478

    Solution:

    The number,7.478478, is non-terminating but recurring, it is a rational number.

    (v) 1.101001000100001…

    Solution:

    Since the number,1.101001000100001…, is non-terminating non-repeating (non-recurring), it is an irrational number.

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