Question 115872



the {{{rational}}}{{{ numbers}}} are the numbers of arithmetic:  the whole numbers, fractions, mixed numbers, and decimals; together with their negative images

A rational number {{{can}}}{{{always}}} be written in what form as a fraction  {{{a/b}}}, where {{{a }}}and {{{b}}} are integers (b is not = 0).


When {{{a}}} and {{{b}}} are positive, that is, when they are natural numbers, then we can always name their ratio.

{{{Only}}} the square roots of square numbers are rational.

An {{{irrational}}}{{{ number}}} is any real number that is {{{not}}} a rational number -- that is, it is a number which {{{cannot}}} be expressed as a fraction {{{a/b}}}, where {{{a}}} and {{{b}}} are integers, with {{{b}}}  non-zero.

If we attempted to express an {{{irrational}}}{{{ number}}} as a complete decimal, then, clearly, we could not, because if we could, the number would be rational.

Examples of both {{{rational}}} and {{{irrational}}} numbers:
{{{sqrt(1) = 1}}},{{{sqrt(4) = 2 }}},{{{sqrt(9) =3}}}……….  rational numbers

{{{sqrt(2) }}}, {{{sqrt(3) }}}, {{{sqrt(5)}}} ,  {{{sqrt(6) }}}  ,  {{{sqrt(7) }}} , {{{sqrt(8) }}}……….   irrational numbers