Question 101305
Is {{{sqrt(77)}}} rational or irrational?
Well, a rational number is a number that can be represented by the quotient of two integers. Examples are: integers, repeating decimals, terminating decimals.
When you take the square root of a number that is not a perfect square, such as {{{sqrt(77)}}}, the result is a non-terminating, non-repeating decimal. Such a decimal can not be represented by the quotient of two integers!
{{{sqrt(77) = 8.77496438739}}}...ad infinitum. This is irrational!