Question

[Simplify Radical Equations].

Answer 1

It'd help both of us if you'd please share whatever work you've done, right or wrong.  Similar or same basic principles apply to all of these problems.  You could learn the pattern and apply it yourself.

1) √125 could be broken down into two factors:  sqrt(5*25) = 5sqrt(5) (ans.)

5)√216  Think:  perfect square factors include 1, 4, 9, 16, 25, 36, 49, 81, 100, 121, etc.    Which of these perfect squares divide into 216 with no remainder?  We want the largest such square.  It is 36.  Therefore, 
sqrt(216) = sqrt(36*6) = 6sqrt(6) (answer)

9)√147  Think:  what is the largest perfect square factor of 147?  Look at the list above (Problem 5).  How about 49?    Then sqrt(147) = sqrt(49)*sqrt(3), or 7sqrt(3).

Please choose 2 of the remaining problems.  Follow my examples.  Share your work.  I'll return if at all possible and continue to help you.

Answer 2

sqrt(216) = sqrt(36*6) = 6sqrt(6)

thats for number five