SOLUTION: I am suppose to simplify quotients containing radicals by rationalizing the denominator. Problem: 30 over square root of 18 problem: 9 over 2 square root 45 Problem: 3 square ro

Algebra ->  Radicals -> SOLUTION: I am suppose to simplify quotients containing radicals by rationalizing the denominator. Problem: 30 over square root of 18 problem: 9 over 2 square root 45 Problem: 3 square ro      Log On


   

Question 108372: I am suppose to simplify quotients containing radicals by rationalizing the denominator.
Problem: 30 over square root of 18
problem: 9 over 2 square root 45
Problem: 3 square root 6 over square root 2
please help
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify quotients containing radicals by rationalizing the denominator.
:
We multiply each expression by the denominator over itself (same as 1)
;
30%2Fsqrt%2818%29 * sqrt%2818%29%2Fsqrt%2818%29 = 30sqrt%2818%29%2F18
:
We can extract a square:
30sqrt%289%2A2%29%2F18 = 30%2A3sqrt%282%29%2F18 = 90sqrt%282%29%2F18
18 cancels into 90
5sqrt%282%29 is the simplified answer
:
:
9%2F2sqrt%2845%29 * sqrt%2845%29%2Fsqrt%2845%29 = 9%2Asqrt%2845%29%2F2%2845%29 = 9%2Asqrt%289%2A5%29%2F90 = 9%2A3sqrt%285%29%2F90 = 27sqrt%285%29%2F90
:
Reduce the fraction divide by 9
3sqrt%285%29%2F10
:
:
3sqrt%286%29%2Fsqrt%282%29 * sqrt%282%29%2Fsqrt%282%29 = 3sqrt%2812%29%2F2 = 3sqrt%284%2A3%29%2F2 = 3%2A2sqrt%283%29%2F2
Cancel out 2:
3sqrt%283%29