SOLUTION: Find three different irrational numbers between the rational number 5/7 and 9/11.

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Question 636813: Find three different irrational numbers between the rational number 5/7 and 9/11.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Square roots of non-squares are irrational.
Square roots of numbers between those two numbers will be between them,
So let's find some non-squares between their squares, and get their square
roots:

Their squares are:

%285%2F7%29%5E2 = 0.5102040816

%289%2F11%29%5E2 = 0.6694214876

Some non-squares between those are 

2/3 = 0.66666667
3/5 = 0.6
4/7 = 0.571428
5/8 = 0.625
5/9 = 0.55555

Their square roots will be irrational and between 5%2F7 and 9%2F11

sqrt%282%2F3%29 = sqrt%282%2F3%29·sqrt%283%2F3%29 = sqrt%286%29%2F3%29
sqrt%284%2F7%29 = sqrt%284%2F7%29·sqrt%287%2F7%29 = sqrt%284%2A7%29%2F7%29 = 2sqrt%287%29%2F7
sqrt%285%2F8%29 = sqrt%285%2F8%29·sqrt%282%2F2%29 = sqrt%2810%29%2F4%29 
sqrt%285%2F9%29 = sqrt%285%2F9%29 = sqrt%285%29%2F3%29 

Edwin