Question 636813
<pre>
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:

{{{(5/7)^2}}} = 0.5102040816

{{{(9/11)^2}}} = 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 {{{5/7}}} and {{{9/11}}}

{{{sqrt(2/3)}}} = {{{sqrt(2/3)}}}·{{{sqrt(3/3)}}} = {{{sqrt(6)/3)}}}
{{{sqrt(4/7)}}} = {{{sqrt(4/7)}}}·{{{sqrt(7/7)}}} = {{{sqrt(4*7)/7)}}} = {{{2sqrt(7)/7}}}
{{{sqrt(5/8)}}} = {{{sqrt(5/8)}}}·{{{sqrt(2/2)}}} = {{{sqrt(10)/4)}}} 
{{{sqrt(5/9)}}} = {{{sqrt(5/9)}}} = {{{sqrt(5)/3)}}} 

Edwin</pre>