Question 723237

I believe problem number 8 was {{{root(3,25)}}} , which is irrational.
I believe problem number 14 may be {{{root(3,125=5)}}} , which is rational, but if it was {{{3sqrt(125)}}} , then it is irrational
0.2222.... = {{{2/9}}} is a rational number
0.303030....= {{{10/33}}} is a rational number
Irrational numbers generate endless decimals that have no repeating pattern.
Repeating decimals are always rational. To express them as a fraction, you can set up an "equation" and solve it, like this:
{{{x}}}= 0.2222...
{{{10x}}}= 2.2222...
{{{10x-x}}}= 2.2222... - 0.2222... ={{{2}}}
So {{{10x-x=2}}} --> {{{9x=2}}} --> {{{9x/9=2/9}}} --> {{{highlight(x=2/9)}}}
{{{y}}}= 0.303030...
{{{100y}}}= 30.303030...
{{{100y-y}}}= 30.303030... - 0.303030... ={{{30}}}
So {{{100y-y=30}}} --> {{{99y=30}}} --> {{{99y/99=30/99}}} --> {{{y=30/99}}} , which simplifies to {{{highlight(y=10/33)}}}