Lesson: Properties of Roots

Comment on Properties of Roots

If x is a positive integer, is √x an integer?

(1) √(4x) is an integer.

(2) √(3x) is not an integer.
gmat-admin's picture

Hello Tolu, am also study for the GMAT so I decided to contact you. my mail is laoshog@gmail.com.

Hi Brent! I picked the wrong answer for the question below (E). Could you please explain why it is A?

https://gmatclub.com/forum/if-x-is-a-positive-integer-is-x-1-2-an-integer-88994.html

Hi Brent,
Looking at your solution for this question.
https://gmatclub.com/forum/if-x-and-y-are-positive-integers-less-than-266628.html

Great explanation again. I can see for statement 1 you have suggested solving it out. I just modified my approach slightly, its the same answer but just checking if my approach is right.

√x+√y= √x+y
Square both sides
(x+y)+2xy=(x+y)
since x and y are positive integers, the minimum value will be x=1,y=1
so 2xy will be at least 2*1*1=2

This shows LHS is greater by RHS..so not true
gmat-admin's picture

Question link: https://gmatclub.com/forum/if-x-and-y-are-positive-integers-less-than-26...\

Good idea, but there is one small error in your approach.

When we take: √x + √y= √(x+y)
And square both sides, we get: (x+y) + √(2xy) = (x+y) [your solution doesn't have √(2xy)]

Otherwise, your logic is great.

Cheers,
Brent

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