Exercise 1.

e1.jpg
Factor common terms from 4-2 square root 6 .Factor 2 out of 4-2 square root 6 giving 2 parentheses 2- square root 6. Square root 3 multiplied by 2 square parentheses 2- square root 6.then you distribute square root 3 over 2- square root 6 which gives you square root 3 parentheses 2- square root 6 which equals 2 square root 3 - 3 square root 2. The final answer is 2 parentheses 2 square root 3 - 3 square root 3.



Exercise 2.

e2.jpg

First Step: Let's simplify our given radicals
6√2- √12 + 5√8
6√2 stays the same because we cannot simplify it any further
√12 can be simplified to √4√3
5√8 can be simplified to 5√4√2

Second Step: Let's plug in our simplified radicals
6√2- √4√3 + 5√4√2

Third Step: Let's solve each radical by finding the square root if possible, and if so, we can then remove the radical sign!
6√2- 2√3 + 5 x 2 √2

*note in this case we would only be able to solve for √4=2*


Fourth Step: Let's combine like terms
6√2 + 5 x 2 √2 - 2√3
6√2 + 10√2 - 2√3
16√2 - 2√3

*note keep the same sign of given number as is ex. - 2√3*

OUR FINAL ANSWER IS:
16√2 - 2√3

-ibet arana

English feedback by Cyndi. FYI, the word "let's" comes from "let us," so you need the apostrophe because it's a long-forgotten contraction.

Exercise 3.


e3.jpg




Exercise 4.



e4.jpg





Exercise 5.


e5.jpg


Exercise 6.

e6.jpg