SOLUTION: HELP PLEASE!! Give an example of two irrational numbers whose product is an irrational number. AND Give an example of two irrational numbers whose product is a rational number.

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Question 256349: HELP PLEASE!!
Give an example of two irrational numbers whose product is an irrational number. AND Give an example of two irrational numbers whose product is a rational number.
Found 2 solutions by palanisamy, jim_thompson5910:
Answer by palanisamy(496) About Me  (Show Source):
You can put this solution on YOUR website!
Sqrt 2 is an irrational number
2*sqrt2 is an irrational number
Their product sqrt2*2*sqrt2 = 4 is a rational number

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1 Give an example of two irrational numbers whose product is an irrational number.

The numbers sqrt%282%29 and sqrt%283%29 are both irrational and so is sqrt%282%29%2Asqrt%283%29=sqrt%282%2A3%29=sqrt%286%29. So the product of sqrt%282%29 and sqrt%283%29 (both irrational) is sqrt%286%29 (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%282%29 and sqrt%288%29 are irrational, but sqrt%282%29%2Asqrt%288%29=sqrt%282%2A8%29=sqrt%2816%29=4 is clearly rational.


So the product of sqrt%282%29 and sqrt%288%29 (both irrational) is 4 (which is rational).