If x=3/4 and y=1/5, what is the value of sqrt(x^2 + 6x + 9)

Question

If x=3/4 and y=1/5, what is the value of sqrt(x^2 + 6x + 9) - sqrt(y^2 - 2y + 1) ? 

(a)91/20 
(b)59/20 
(c)47/20 
(d)15/4 
(e)14/5

So sorry, I had to edit my Question. Please support your answers with explanations.

GK_Gmat · Answer

Answer B

first sqrt solves to sqrt (x+3)^2, second sqrt solves to sqrt (y-1)^2

Plug in values of x and y to get 15/4-4/5 which is equal to 59/20

ioiio · Answer

I think A

But 

x + 3 - (y-1) = x -y + 4 = 4.55

15/4 -(-4/5) = 

75 + 16
---------
 5

But my problem is 4.55 is not a choice there... even 89/20 is only 4.45 if I am right.

Am I missing something?

ioiio · Answer

I get it

sqrt can be +/-

3.75 -  is also a possible answer. 

So 59/20 makes sense.

ArvGMAT · Answer

59/20 Got to be careful with squares and roots .. i was about to select 91/20 and when u mentioned be careful

thought twice about the answer.

misterJJ2u · Answer

got A

sqrt   = sqrt  = x+3 = (3/4)+3 or 15/4
sqrt  = sqrt  = y-1 = (1/5)-1 or -4/5

so (15/4) - (-(4/5)) = (15/4) + (4/5) = (75/20) + (16/20) =91/20.

what am i missing that people are getting (59/20)?

what's the OA?

emoryhopeful · Answer

I get B. 59/20

Plugging in values I get 15/4 - 4/5 which equals to 59/20

I think the trick is knowing that sqrt(y-1)^2 must be solved inside the parentheses first, before squaring the inside, then taking its square root. If you just have the powers cancel first, you would get 15/4 - (-4/5), thus equaling 91/20 the wrong answer.

ioiio · Answer

Btw, I dont think 91/20 is a wrong answer... Its just not one of the answer choices here. So we were left to find one of more possible right answers.

zakk · Answer

after reading it, I worked it out and got A, little fuzzy on how folks are getting B. 

isn't it 75/20 - (-16/20) ?

Hayabusa · Answer

I guess they are saying that you can't have a negative root.

What's the source of this question?

zakk · Answer

Right. But if we have handled the sqrt by eliminating the ^2 (they cancel don't they or am I really off!?) doesn't it come a moot point?

misterJJ2u · Answer

ahhhh, it clicked.

It's because you are plugging in the numbers for the variables and squaring them BEFORE taking the square root.

That makes sense, I get it and am now a believer in option B. 

Good question.

Can we confirm the OA???

Fig · Answer

Other approaches here : https://www.gmatclub.com/phpbb/viewtopic.php?t=49388 The OA is indeed B

(ajay_gmat : pls, do not post 2 times the same question... thx

)

briks123 · Answer

I remember reading something in Manhattan GMAT that said that for GMAT purposes, the square root is always the positive square root.

If x=3/4 and y=1/5, what is the value of sqrt(x^2 + 6x + 9)

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