SOLUTION: hello, can someone EXPLAIN how do figure out the following: 1/2sqrt5 + 1 1/2sqrt20 = 7/2sqrt5 I appreciate any help on the process. thank you!

Algebra ->  Radicals -> SOLUTION: hello, can someone EXPLAIN how do figure out the following: 1/2sqrt5 + 1 1/2sqrt20 = 7/2sqrt5 I appreciate any help on the process. thank you!      Log On


   

Question 752286: hello, can someone EXPLAIN how do figure out the following:
1/2sqrt5 + 1 1/2sqrt20 = 7/2sqrt5
I appreciate any help on the process. thank you!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Assume the problem is:
1%2F2sqrt%285%29 + 1 1%2F2sqrt%2820%29 = 7%2F2sqrt%285%29
Make the 1 and 1/2 an improper fraction
1%2F2sqrt%285%29 + 3%2F2sqrt%2820%29 = 7%2F2sqrt%285%29
multiply the equation by 2, this gets rid of the denominators
sqrt%285%29 + 3%2Asqrt%2820%29 = 7%2Asqrt%285%29
Factor inside the middle radical to reveal a perfect square
sqrt%285%29 + 3%2Asqrt%284%2A5%29 = 7%2Asqrt%285%29
Extract the square root of 4
sqrt%285%29 + 3%2A2%2Asqrt%285%29 = 7%2Asqrt%285%29
sqrt%285%29 + 6%2Asqrt%285%29 = 7%2Asqrt%285%29
they are like terms now sqrt(5) just add
7%2Asqrt%285%29 = 7%2Asqrt%285%29 which is obviously true