Question
State whether the following statements are 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 , where is a natural number.
(iii) Every real number is an irrational number.
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Text solutionVerified
(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 , where is a natural number.
(iii) False: All numbers are real number and non terminating numbers are irrational number.
For example etc. are some example of real numbers and these are not irrational.
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Question Text | State whether the following statements are 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 , where is a natural number. (iii) Every real number is an irrational number. |
Answer Type | Text solution:1 |
Upvotes | 150 |