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## Comment on

Properties of Roots## If x is a positive integer,

(1) √(4x) is an integer.

(2) √(3x) is not an integer.

## Here's my step-by-step

Here's my step-by-step solution: https://gmatclub.com/forum/if-x-is-a-positive-integer-is-x-1-2-an-intege...

Cheers,

Brent

## Hello Tolu, am also study for

## Hi Brent! I picked the wrong

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

## Question link: https:/

Question link: https://gmatclub.com/forum/if-x-is-a-positive-integer-is-x-1-2-an-intege...

Here's my full solution: https://gmatclub.com/forum/if-x-is-a-positive-integer-is-x-1-2-an-intege...

Cheers,

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

## Question link: https:/

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

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

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

i will keep this noted.

## Question link: https:/

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

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

## 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:

https://www.youtube.com/watch?v=D__dWwmgq2w&t=7s

Thanks,

## That video can be found here:

That video can be found here: https://www.gmatprepnow.com/module/general-gmat-strategies/video/1113

Here are some similar mental math videos:

- Dividing by 5: https://www.gmatprepnow.com/module/general-gmat-strategies/video/1112

- Squaring numbers with units digit 5: https://www.gmatprepnow.com/module/gmat-powers-and-roots/video/1024

- finding x% of y: https://www.gmatprepnow.com/module/gmat-arithmetic/video/1076

Cheers,

Brent