Algebra square root problems :( simplify equations then solve with steps

Question

I am totally stumped on these problems :/ please help and show steps so I can understand these problems with square roots and other that will come along in algebra, thank you :)

first simplify all all problems showing steps, then solve simplified equation also showing your steps. Thank you c:

1.) √(24/6)-√(6)

2.) √(4z)+(15)+(9)=-√(225)

3.) √(75t^3/3tv^4)

3.) (5)+(6)√(7)^2

4.) √(1/2) (c)+(6)=√(3c)-(9)

5.) (7x/√x)-(8√x/2)

6.) (3)√(2)+(y)=√(18)

7.) √(80b^2)-(b)√(125)

 

Also please simplify the following problem 

 

8.) (3)+√(3)/(5)-√(5) ((5)+√(5)/(5)+√(5)) = (15)+√(15)/(25)-(5) =(15)+√(15)/(20)

 

thank you for your support and helping me understand these steps in further problems c:

Answer 1

1.) (√24/6-√6)  simplify the square root of 24 by factoring its radicand; choose 4 times 6 = 24 but square root of the 4 is 2, so 2√6 replaces square root of 24.  So this expression becomes (2/6)√6 - √6  = √6 [1/3 - 1] = -(2/3)•√6

 

4.) √(1/2 c+6=√3c-9 is an equation; we should solve for c. BUT there's a missing parenthesis, so exactly what is intended isn't clear.

 

Many of these contain the defect that the scope of the square roots is not clear.In this platform, radicands need to be enclosed in parentheses in order to show exactly what the square root is to be applied to.