SOLUTION: insert two irrational numbers between root 2 and root 3

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Question 757481: insert two irrational numbers between root 2 and root 3
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Number_______________Number_Squared
2____________________4
3____________________9

Look at this in the other direction. sqrt%284%29 is 2.
sqrt%289%29 is 3. Can you find any squares between 4 and 9? No. Can you find some numbers between 4 and 9? Yes.

Pick any number between 4 and 9 EXCLUDING 4 and 9. Would the square root be rational or irrational? Would this square root be within the limits of between 2 and 3 or not?
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And if that did not give you clear enough impression for finding irrational numbers between 2 and 3, let us see an expansion of the above table:

Number_______________Number_Squared
2____________________4
?____________________4.3
?____________________4.77
?____________________5
?____________________6
?____________________6.51
?____________________6.94
?____________________7
?____________________8
3____________________9