# Lesson: Properties of Roots

## Comment on Properties of Roots

### If x is a positive integer,

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

(1) √(4x) is an integer.

(2) √(3x) is not an integer.

### Hello Tolu, am also study for

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

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,

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

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)]

Cheers,
Brent

### https://gmatclub.com/forum/1

https://gmatclub.com/forum/1-199916.html

I'm stupid enough to ignored the root so I got 10000....

i will keep this noted.

The good thing is that the mistake happened while practicing (not during the real deal!)

### Hello,

Hello,
I'm writing to you to kindly ask in which module I can find this video (and tips like this one) related to the first exercice: