Question

find two rational and irrational between between 2 and 3 in decimal form

Answer 1

Step-by-step explanation:

We know that the value of the square of 2 is 4 and the value of the square of 3 is 9. Simplifying the above expressions, we get: 2<√6<3. Hence, the two irrational numbers between 2 and 3 are √6 and √7.

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Answer 2

Step-by-step explanation:

How can I find two irrational numbers between 2 and 3?

One interesting twist to this question is something cropping up in music theory all the time, that has to do with equitable intervallic subdivision, also called a (generalized) equal temperament: find two (irrational?) numbers between 2 and 3 that are logarithmically equidistant.

To make it sound as simple as musicians know, understand, mean and have been practising it from time immemorial, it goes as follows. First of all, ratio 3/2 of frequencies (or, equivalently, as the Pythagoreans had it, inverted ratio of string segment lengths) is the perfect fifth. How do I split the interval of a fifth into three (or k, for that matter,) “equal” intervals, i.e. into three pieces that sound like “the same (transposed) interval” to the human (and every other mammalian) ear, given that intervals are perceived as ratios of frequencies?

What we do first is take the third (kth in the general case) root of our ratio, i.e. ³√(3/2), and that will be irrational as long as the original interval is not a perfect cube (/kth power); 3/2 isn’t a perfect cube.