SOLUTION: Explain why the product of two conjugates never contain a square root. Thanks for your time and help with this explaination. Ramona

Algebra ->  Square-cubic-other-roots -> SOLUTION: Explain why the product of two conjugates never contain a square root. Thanks for your time and help with this explaination. Ramona      Log On


   

Question 391510: Explain why the product of two conjugates never contain a square root.
Thanks for your time and help with this explaination.
Ramona
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose a and b are real numbers where b is not necessarily a perfect square. Then the product

%28a+%2B+sqrt%28b%29%29%28a+-+sqrt%28b%29%29 is equal to

a%5E2+%2B+a%2Asqrt%28b%29+-+a%2Asqrt%28b%29+-+b The square root terms cancel out.

= a%5E2+-+b