OG10 222

[mitzi]

If X is a positive integer, is sqrt X an integer?
1) sqrt 4x is an integer
2) sqrt 3x is not an integer

OG's explanation got me lost. it says that "sqrt 4x is an integer, it follows that 4x must be the square of an integer, and so x must be the square of an integer. therefore sqrt x must be integer"

I am lost... please help me get out of this jungle....

[finsisher]

IMO A

since 4 is an integer so sqrt x is integer...

[nverma]

Originally Posted by mitzi

If X is a positive integer, is sqrt X an integer?
1) sqrt 4x is an integer
2) sqrt 3x is not an integer

OG's explanation got me lost. it says that "sqrt 4x is an integer, it follows that 4x must be the square of an integer, and so x must be the square of an integer. therefore sqrt x must be integer"

I am lost... please help me get out of this jungle....

Hi Mitzi

when we say sqrt(4x) is integer..We understand that 4x is a perfect square..
Lets assume some values of x, x=1,2,3, 4,....25,...64...100.
4x can only be perfect square when x is also a perfect square..bcoz 4 is already a perfect square.

So x has to be a perfect square..

x is an integer..If x would have been any positive number,, then the story would have been different..

Let say x=6.25.. Now 4x= 25 ..so sqrt(4x)=5.. but sqrt(x) is not an integer..

So till the time x is integer the answer is A..