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State whether the following statements af true or false. Justify your answers.
(i) Every irrational number is a real number.
(ii) Every point on the number line is of the form \( \sqrt{m} \), where \( m \) is a natural number
(iii) Every real number is an irrational number.
Solution:
i) True: Real numbers are any number which can we think.
Thus, every irrational number is a real number.
ii) False: A number line may have negative or positive number.
Since, no negative can be the square root of a natural number, thus every point the the number line cannot be in the form of √m
iii) False: All numbers are real number and non terminating numbers are irrational number.
For example 2,3,4, etc. are some example of real numbers and these are not irrational.
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