SOLUTION: Simplify each radical expression. {{{(sqrt(3)+5)(sqrt(3)-3)}}} I am having difficulty simplifying radical expressions and need some additional help and understanding on how to

Algebra ->  Square-cubic-other-roots -> SOLUTION: Simplify each radical expression. {{{(sqrt(3)+5)(sqrt(3)-3)}}} I am having difficulty simplifying radical expressions and need some additional help and understanding on how to       Log On


   

Question 74302This question is from textbook Beginning Algebra
: Simplify each radical expression.
%28sqrt%283%29%2B5%29%28sqrt%283%29-3%29
I am having difficulty simplifying radical expressions and need some additional help and understanding on how to do these. Thanks This question is from textbook Beginning Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%283%29%2B5%29%28sqrt%283%29-3%29
sqrt%283%29%2Asqrt%283%29-3%2Asqrt%283%29%2B5%2Asqrt%283%29-15
3-3%2Asqrt%283%29%2B5%2Asqrt%283%29-15Since sqrt%283%29%2Asqrt%283%29 is the same as %28sqrt%283%29%29%5E2 we can say that sqrt%283%29%2Asqrt%283%29=3
3%2B%28-3%2B5%29%2Asqrt%283%29-15Add like terms. In this case sqrt%283%29 is the common term. If we letx=sqrt%283%29 the it looks like -3x%2B5x=%28-3%2B5%29x=2x
3%2B2%2Asqrt%283%29-15Finally add -15 to 3
2%2Asqrt%283%29-12There's your simplified answer


Check:
%28sqrt%283%29%2B5%29%28sqrt%283%29-3%29Numerically evaluate the given expression
%281.73%2B5%29%281.73-3%29
%286.73%29%28-1.268%29
-8.536
2%2Asqrt%283%29-12
2%281.73%29-12
3.464-12
-8.536This shows that our simplified answer works.