kaplan 49

you should rephrase the statements before you do anything else, because they're both fantastically easy equations to solve. if you solve them, you get the following rephrases:
(1) x = 4 or 10
(2) x = 4

note that (2) is automatically SUFFICIENT, because it's one number; because it's one value, that number is guaranteed to give either a 'definitive yes' answer or a 'definitive no' answer.

to determine whether (1) is sufficient, just plug 4 and 10 into the equation and see what happens:
x = 4 --> rad(16) = 2 + rad(4) --> yes
x = 10 --> rad(22) = 2 + rad(10) --> no
INSUFFICIENT, because you have a 'yes' and a 'no'

note that there's no need to solve the equation, because the answer choices are so easy to rephrase!

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Enginpasa1 wrote:does root (x+12) = 2 + Root X
I squared the whole thing and the book only square the left side. Is that even possible. I thought what you do to one side you must do to another side.

if you insist on solving the equation - which is, frankly, a waste of time, as you can just plug in the answer choices as is done above - then yes, you are absolutely right: you need to square both sides.

x + 12 = 4 + 4rad(x) + x
8 = 4rad(x)
2 = rad(x)
4 = x
so, the question rephrases to ... is x = 4?