Math  Help with radicals please
posted by Anonymous on .
Please show work
Simplify rational
1. 4√(a^6 b^13) / 4√(a^2b)
2.√(2x^3 / 49y^4)
Add or Subtract
3. x√(75xy)  √(27x^3y)
Multiply
4.(√(5)  5) (2√(5) + 2)
Rationalize the denominator
5. √(25x^5 / 3y^2)
6. 5 / 2√(7)

do you have any idea how to do any of these or where to start??

I know the basics but I'm still not solid on the concepts. I mainly want to see the processes. Any help would be really appreciated.

Also in number 5 it's 24 not 25 sorry.

It seems that you need a lesson in everything you need to know about radicals.
#3 You can't combine radicals unless they are the same like 3x  2x = 1x
So yo have to write 75 xy as 25(3xy) you can take the square root of 25 with the 3xy left under the radical. for 27x^3y write it as 9x^2(3xy) Take the square root of 9x^2 and the 3xy is left under the radical. Now. you have like terms. Keep the radical 3xy and combine what is out in front.
#4 multiply that one like you woud (x 5)(2x +2) It works like multiplying binomials. It gets a little more confusing because of the radical. Remember square root of 5 times square root of 5 is 5.
#5 put the radical over the numerator and over the denominator. Multipy the numerator and denominator by the square root of 3y^2. When you multiply square root of 3y^2 times square root of 3y^2 you will get just 3y^2.
#6 multiply the numertor and the denominator by the conjugate which is
2 +(radical 7). 
#3 I got 2ab^2 3√(3a^2b)
In #4 I'm not really sure how to multiply the radical is the problem, it's the FOIL method but I still don't really know how to handle it with a radical instead.