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# If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)

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Joined: 11 Sep 2015
Posts: 4345
Re: If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

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22 Apr 2018, 05:15
Top Contributor
1
dave13 wrote:
hello there GMATPrepNow

can you please explain how you combine both statements to get answer

Statement 1 tells us that x + y = 15
Statement 2 tells us that √(xy) = 6

and then you say Recognize that (√x + √y)² = x + 2√(xy) + y

I dont recognize this pattern in either of the statements how can I recognize it looking at both statements where did you get this formula ?

I thought I should do square both sides of √(xy) = 6 so I am getting xy = 36 and also have x + y = 15 so I do something like this

x + y = 15 ---> x = 15-y and plug in here xy = 36

thank you in advance for taking time to explain and have a great gmat weekend

It's not easy to see that (√x + √y)² = x + 2√(xy) + y, however when we see that we have information about x and y and we need to find the value of √x and √y and y, we might start looking for possible relationships that might help us. One relationship is that (√x)² = x and that (√y)² =y
From there, it's a matter of exploring what (√x + √y)² might look like.
We can use the FOIL method to expand (√x + √y)²
We get: (√x + √y)² = (√x + √y)(√x + √y) = x + √xy + √xy +y = x + 2√xy + y
At this point, we can see that our exploration has paid off.

Keep in mind that solving math questions involves little explorations like this. Sometimes those explorations take us closer to the solution; sometimes they take us nowhere, in which case we need to try something else.

Cheers,
Brent
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Re: If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

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08 May 2018, 08:29
(√x+√y)^2= x +y +2√xy

All needed info is present in two statements

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Re: If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

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27 Jul 2018, 00:23
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Bunuel wrote:
If x and y are positive integers, what is the value of $$\sqrt{x} + \sqrt{y}$$?

(1) x + y = 15
(2) $$\sqrt{xy}= 6$$

Kudos for a correct solution.

(1) 9+6=15
or, 12+3= 15
So, insufficient

(2) xy = 36
Which is : 4*9 = 36
12*3 = 36
So, there are two values of x and y.
insufficient.

Considering (1) and (2) x
([m]\sqrt{x} + \sqrt{y}[/m)^2= x+ y+2 [m]\sqrt{xy}
= 15+2.6
= 27
So, Ans is C.
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Re: If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

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21 May 2019, 09:22
I thought that that the GMAT requieres only unique solution. In this case √x + √y = ± √27 . Please help
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If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)  [#permalink]

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16 Sep 2019, 03:52
Bunuel wrote:
If x and y are positive integers, what is the value of $$\sqrt{x} + \sqrt{y}$$?

(1) x + y = 15
(2) $$\sqrt{xy}= 6$$

Kudos for a correct solution.

If x and y are positive integers, what is the value of $$\sqrt{x} + \sqrt{y}$$?

$$\sqrt{x} + \sqrt{y} =\sqrt{(x+y+2\sqrt{xy})}$$

(1) x + y = 15
NOT SUFFICIENT

(2) $$\sqrt{xy}= 6$$
NOT SUFFICIENT

(1) + (2)
(1) x + y = 15
(2) $$\sqrt{xy}= 6$$
$$\sqrt{x} + \sqrt{y} =\sqrt{(x+y+2\sqrt{xy})} = \sqrt{(15+2*6)} = \sqrt{27}$$
Since x & y are positive integers, $$\sqrt{x} + \sqrt{y}$$ is positive

SUFFICIENT

IMO C
If x and y are positive integers, what is the value of x^(1/2)+y^(1/2)   [#permalink] 16 Sep 2019, 03:52

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