Question 256349
# 1 Give an example of two irrational numbers whose product is an irrational number.


The numbers {{{sqrt(2)}}} and {{{sqrt(3)}}} are both irrational and so is {{{sqrt(2)*sqrt(3)=sqrt(2*3)=sqrt(6)}}}. So the product of {{{sqrt(2)}}} and {{{sqrt(3)}}} (both irrational) is {{{sqrt(6)}}} (which is also irrational).



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# 2  Give an example of two irrational numbers whose product is a rational number


The numbers {{{sqrt(2)}}} and {{{sqrt(8)}}} are irrational, but {{{sqrt(2)*sqrt(8)=sqrt(2*8)=sqrt(16)=4}}} is clearly rational.



So the product of {{{sqrt(2)}}} and {{{sqrt(8)}}} (both irrational) is {{{4}}} (which is rational).