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Q: Irrational numbers between 2 and 2.5?

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2

Infinitely many. In fact, there are more irrational numbers between 1 and 2 as there are rational numbers - in total. The cardinality of this set is Aleph-0ne.

No. sqrt(3) - sqrt(2) is irrational.

4*sqrt(2) Rational multiples of irrational numbers are irrational. sqrt(2) is about 1.414, and 5/4 = 1.25 < 1.414... < 1.75 = 7/4 so 4*sqrt(2) is between 5 and 7, and is irrational.

The difference can be rational or irrational.5 + sqrt(3) and 2 + sqrt(3) are both irrational numbers but their difference is[5 + sqrt(3)] - [2 + sqrt(3)] = 3, which is rational.

Related questions

There are an infinite number of irrational numbers between 2 and 4. See the link below for the definition of irrational numbers. The two most popular irrational numbers between 2 and 4 are pi (3.14159...) and e (2.71828...).

2

Infinitely many. In fact, there are more irrational numbers between 1 and 2 as there are rational numbers - in total. The cardinality of this set is Aleph-0ne.

There are infinitely many irrational numbers between sqrt(2) and sqrt(3).

Irrational numbers are infinitely dense. this means that there are infinitely many irrational numbers between any two numbers and so the term "next" has no meaning.

No, there are more irrational numbers between 1 and 2 than there are rational numbers.

No, not at all. There are more irrational numbers between 1 and 2 than there are rational numbers in total!

sqrt(2), sqrt(3)

No. sqrt(3) - sqrt(2) is irrational.

4*sqrt(2) Rational multiples of irrational numbers are irrational. sqrt(2) is about 1.414, and 5/4 = 1.25 < 1.414... < 1.75 = 7/4 so 4*sqrt(2) is between 5 and 7, and is irrational.

The difference can be rational or irrational.5 + sqrt(3) and 2 + sqrt(3) are both irrational numbers but their difference is[5 + sqrt(3)] - [2 + sqrt(3)] = 3, which is rational.

[ square root of (2) ] is irrational

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