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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?

  1. 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.

  2. 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.

bau8312
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  • If you typed the question right, D is the correct answer. – user3010768 May 02 '20 at 06:20
  • @user3010768 added a photo of the exam excercise, Im pretty sure I typed the questio right but just in case I missed something – bau8312 May 02 '20 at 06:30
  • Yeah, it's right, I was thinking if you had written the roots too long (which wouldn't have made B the right answer either).

    So, the last one is the correct answer.

     – user3010768 May 02 '20 at 06:41
  • @user3010768 ups that was a typo, he choose C as the answer – bau8312 May 02 '20 at 06:43
  • I think $15 \sqrt {2t} - 14\sqrt t$ is indeed the best answer. As it is not a choice, $15 \sqrt {2t} - 7\sqrt {4t}$ is the best option. As for your friends work, $5(2t)^{\frac 12} \ne 10 t^{\frac 12}.$ You can't just take the 2 out from under the exponent like that. – Doug M May 02 '20 at 06:48
  • It's still a wrong answer. $7\sqrt{4t} =14\sqrt{t}$ like you said, so they can't be subtracted from $\sqrt{2t}$s as such. You'd get $(15\sqrt{2}-14)\sqrt{t}$. – user3010768 May 02 '20 at 06:49
  • You are right. The other student and the teacher are wrong. Of the four choices $15\sqrt {2t} - 7\sqrt{4t}$ is the only one that is correct. However the instructions were to "simplify" and $15\sqrt{2t}-7\sqrt{4t} = 15\sqrt{2t}-14\sqrt t$ is a further simplification so I'd so D) isn't a complete answer. – fleablood May 02 '20 at 07:49
  • "I think he messed up here, shoudln't this be" in this case you are both wrong it should be $52^{\frac 12}t^{\frac 12} - 74^{\frac 12}t^{\frac 12} + 102^{\frac 12}t^{\frac 12} = 152^{\frac 12}t^{\frac 12} - 14t^{\frac 12} = 15\sqrt{2t} - 14\sqrt t$. – fleablood May 02 '20 at 07:55
  • @fleablood yes I was editing that just now – bau8312 May 02 '20 at 08:00

3 Answers3

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It is $D$, clearly. You can find this yourself by eliminating other 3 cases:

What you get if, say $t=0$ and if $t=1$?

nonuser
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Put $t\rightarrow t^2$ throughout, and it comes to $$ 15 \sqrt 2 t- 14 t $$ Hence option D.

Narasimham
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The answer is D. The second student made the same mistake in each term of the expression. He move the constant out of the parenthesis without taking into account the exponent. For example $7*(4t)^{1/2} = 7*4^{1/2}*t^2=2*2*t^{1/2} = 14(t)^{1/2}$ it is not $28(t)^(1/2$)

Harish Chandra Rajpoot
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Letty
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