SOLUTION: {{{10 sqrt (1/5) - sqrt (45) - 12 sqrt (5/9)}}} I have tried rationalizing the denominators and mutliplying by either radical 5 or 3 radical 5, but am struggling with what to do

Algebra ->  Radicals -> SOLUTION: {{{10 sqrt (1/5) - sqrt (45) - 12 sqrt (5/9)}}} I have tried rationalizing the denominators and mutliplying by either radical 5 or 3 radical 5, but am struggling with what to do      Log On


   

Question 751341: 10+sqrt+%281%2F5%29+-+sqrt+%2845%29+-+12+sqrt+%285%2F9%29
I have tried rationalizing the denominators and mutliplying by either radical 5 or 3 radical 5, but am struggling with what to do with the whole numbers before the sqrt when I do that.
Also tried making this into improper fractions, but was again foiled with the initial 10 and then the 1 over sqrt 5.
Hope you can help me.
Found 2 solutions by ankor@dixie-net.com, josgarithmetic:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
10%2Asqrt%281%2F5%29+-+sqrt%2845%29+-+12%2Asqrt%285%2F9%29
:
Try to extract square roots to end up with like terms, square root of 5:
:
sqrt%28100%2F5%29+-+sqrt%289%2A5%29+-+%281%2F3%29%2A12%2Asqrt%285%29
:
sqrt%2820%29+-+3%2Asqrt%285%29+-+4%2Asqrt%285%29
:
sqrt%284%2A5%29+-+3%2Asqrt%285%29+-+4%2Asqrt%285%29
:
2%2Asqrt%285%29+-+3%2Asqrt%285%29+-+4%2Asqrt%285%29
:
-5%2Asqrt%285%29

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
10+sqrt+%281%2F5%29+-+sqrt+%2845%29+-+12+sqrt+%285%2F9%29

Let us look at just the square roots having the irrational denominators.

*
sqrt%281%2F5%29=1%2Fsqrt%285%29


*
sqrt%285%2F9%29=sqrt%285%2F%283%2A3%29%29=highlight%28sqrt%285%29%2F3%29


Your expression should now be worked into this:
highlight%2810%2Asqrt%285%29%2F5-sqrt%285%2A9%29-12%2Asqrt%285%29%2F3%29
and that should now be easier to finish simplifying.