Question

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)

Answer 1

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

Answer 2

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.

Answer 3

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

Answer 4

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).

Answer 5

#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.