Question

[Simplify Radical Equations].

This is a reworded version of my previous question, I messed up on the past one.
I'm having a bit of difficulty figuring these out, I know it's easy but every time I try to look it up, the answers don't match the choices. Please answer any of the ones you can figure out. (You can use one choice more than once.)

1) √125.
2) √216.
3) √512.
4)√405.
5)√216.
6)√100.
7)√80.
8)√45.
9)√147.
10)√200.
11)√75.
12)√64.
13)√800.
14)√28.
15)√288.
16)√384.
17)√96.
18)√72.
19)√150.
20)√80
21)√125
22)√24
23)√192
24)√8
25)√216
26)√24
27)√16
28)√48
29)√75
30)√500

Choices
4
9
16
25
36
49
64
81
100
121
144
169
196
225
256
289
324
361
400

Sorry for all the questions, just please answer as many as possible, thanks

Answer 1

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

thats for number five

Answer 2

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.