Question

what do you do to check wheater a number is rational or irrational? in your explanation use an example of an irrational and a rational number.

Answer 1

a number which can be written in the form p/q where p and q are integers.
e.g \[2=\frac{ 2 }{ 1 },-3=\frac{ -3 }{ 1 },1.3=\frac{ 13 }{ 10 },0.666.....=\frac{ 2 }{ 3 }\]
are rational numbers.
\[\sqrt{7},\sqrt{2},\pi ~etc.~are~irrational~numbers.\]

Answer 2

Well by definition, rational numbers are fractions. that is, numbers that can be expressed as a ratio of two integers
\[\frac{ 5 }{ 4 }\]
or \[\frac{ 8 }{ 3 }\]
or \[\frac{ 239487293 }{ 238492837982 }\]
these are all rational numbers
Usually, irrational numbers are numbers that involve square roots, like:
\[\sqrt2\] or \[\sqrt20\]
irreducible square roots are irrational numbers

Other examples of irrational numbers are the famous constants, pi and e
these are also irrational - cannot be expressed as a ratio of two integers

Answer 3

thanks

Answer 4

yw :)