Hence #sqrt7#, #root(3)17#, #root(4)54# and also #root(5)178# room all irrational numbers between #2# and #3#,

as #4; #8; #16 and also #32.

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For other methods of finding such numbers view What are three numbers in between 0.33 and also 0.34? Adding on come the other answer, us can easily generate as many such numbers as we"d prefer by noting the the sum of one irrational through a reasonable is irrational. Because that example, we have actually the well known irrationals #e =2.7182...# and #pi = 3.1415...#.

So, without worrying around the exact bounds, we deserve to definitely add any optimistic number much less than #0.2# to #e# or subtract a hopeful number less than #0.7# and also get another irrational in the wanted range. Similarly, we can subtract any type of positive number in between #0.2# and also #1.1# and get an irrational between #2# and also #3#.

#2

#2

This have the right to be done with any type of irrational because that which we have actually an approximation because that at least the integer portion. Because that example, we understand that #1 . Together #sqrt(2)# and #sqrt(3)# space both irrational, us can add #1# to either of them come get additional irrationals in the preferred range:

#2 EET-AP
Aug 9, 2017

Irrational numbers room those that never provide a clean result. 3 of those between #2 and also 3# might be: #sqrt5, sqrt6, sqrt7#, and there room many much more that go past pre-algebra.

Explanation:

Irrational numbers are always approximations of a value, and each one tends to walk on forever. Roots of every numbers that space not perfect squares (NPS) are irrational, as are some valuable values choose #pi# and also #e#.

To discover the irrational numbers in between two numbers prefer #2 and 3# we need to an initial find squares that the two numbers which in this situation are #2^2=4 and also 3^2=9#.

Now we know that the start and also end clues of our collection of possible solutions space #4 and 9# respectively. We additionally know the both #4 and 9# room perfect squares due to the fact that squaring is how we discovered them.

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Then using the definition above, we deserve to say that the root of every NPS numbers in between the two squares us just found will it is in irrational numbers in between the original numbers. In between #4and9# we have actually #5, 6, 7, 8#; who roots space #sqrt5, sqrt6, sqrt7, sqrt8.#

The roots of these will certainly be irrational numbers between #2 and 3#.