SOLUTION: hi, i need help on simplifying radical expressions with sqaure roots. They're are three different types of problems on my homework and i dont know how to solve them. I'm wondering

Algebra ->  Radicals -> SOLUTION: hi, i need help on simplifying radical expressions with sqaure roots. They're are three different types of problems on my homework and i dont know how to solve them. I'm wondering      Log On


   

Question 30186: hi,
i need help on simplifying radical expressions with sqaure roots. They're are three different types of problems on my homework and i dont know how to solve them. I'm wondering if they are solved the same way and how to solve them...some examples on my homework are.... +sqrt%28+20+%29+.... +sqrt%28+125a+%29+....and +sqrt%28+3x+to+the+second+power%2B30xy%2B75y+to+the+second+power+%29+...it will be very appreciated if you help me...thanks
-kelsey larue
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
Since we are working square roots, work to the prime factors an pull them out 2 at a time
+sqrt%28+20+%29+ or +2%2A2%2A5++ or +%282%29sqrt%285%29+
+sqrt%28+125a+%29+ or +5%2A5%2A5%2Aa+ or +%285%29+sqrt%285a%29+
since this next one is a trinomial ... we need to work that part first.
+sqrt%28+3x%5E2+%2B+30xy+%2B+75y%5E2+%29+ factor the trinomial
+3x%5E2+%2B+30xy+%2B+75y%5E2+ factor out a 3
+3%28x%5E2+%2B10xy+%2B25y%5E2%29+ the new trinomial is still factorable and is in fact a perfect square
+3%28x%2B5%29%28x%2B5%29+ place it back in the root
+sqrt%28+3%28x%2B5%29%28x%2B5%29+%29+ take out a pair
+%28x%2B5%29sqrt%28+3+%29+