How many irrational numbers are there between 1 and 6?
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Answered by
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There are infinitely many irrational numbers between 1 and 6.
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22
Between any two numbers, however large or small the difference between them may be, we have infinite rational as well as irrational numbers. As such between 1 and 6 too we have infinite irrational numbers.
Irrational numbers in their decimal form are non-repeating and non-terminating numbers. Hence say between 1 and 1.01, we can construct infinite irrational numbers like 1.00001000100001......., 1.01001000200003.......
1.00002000200002........
1.00003000300003....... and so on.
Similarly, between any two rational numbers a and b, we can have a+b2, a rational number and then between a and a+b2 as well as a+b2 and b, we can construct more rational numbers. And repeating this we can have infinite rational numbers between any two rational numbers.
Irrational numbers in their decimal form are non-repeating and non-terminating numbers. Hence say between 1 and 1.01, we can construct infinite irrational numbers like 1.00001000100001......., 1.01001000200003.......
1.00002000200002........
1.00003000300003....... and so on.
Similarly, between any two rational numbers a and b, we can have a+b2, a rational number and then between a and a+b2 as well as a+b2 and b, we can construct more rational numbers. And repeating this we can have infinite rational numbers between any two rational numbers.
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