Q:

Simplifiy radicals

I took an algebra exam today and came across this problem

Simplify: $ 5\sqrt{2t} - 7\sqrt{4t} + 10\sqrt{2t} $
A. $\sqrt{t}$
B. $\sqrt{2}$
C. $\sqrt{2t}$
D. $15\sqrt{2t} - 7\sqrt{4t} $

Two different approaches give two different results?

I did this, add like terms $ 5\sqrt{2t} +10\sqrt{2t} =  15\sqrt{2t} $
$ 5\sqrt{2t} - 7\sqrt{4t} + 10\sqrt{2t} $
$ 15\sqrt{2t} - 7\sqrt{4t} $ last term could be simplify to $- 14\sqrt{t}  $ but it isn't an option in the test.
Another student did this, converting radicals to exponencials first
$ 5\sqrt{2t} - 7\sqrt{4t} + 10\sqrt{2t} $
$ 5(2t)^{1/2} - 7(4t)^{1/2} + 10(2t)^{1/2} $
$ 10t^{1/2} - 28t^{1/2} + 20t^{1/2} $ I think he messed up here
$ 2t^{1/2}  = \sqrt{2t}$ also shouldn't this be $ 2t^{1/2}  = 2\sqrt{t}$ ?

I chose D as the answer and he chose C, I failed that question and he didn't, am I wrong? Explain please.

A:

It is $D$, clearly. You can find this yourself by eliminating other 3 cases:
What you get if, say $t=0$ and if $t=1$?

