X is divisible by 144. 3 sqrt x is an integer, then which of the following 3 sqrt x definitely divisible by? (Choose all that apply)
A) 4
B) 8
C)9
D)12
[spoiler]A & D[/spoiler]
Thanks!
Divisibility Question
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i get A, C and D
x/144=k (integer) 144=2^4*3^2
the minimum that x can be 2^4*3^2 (x not zero, as sq. root defined over positive numbers)
if minumum x=2^4*3^2; sq root x is 2^2 *3
3 sqrtx =2^2*3^2 at aleast.
A. 2^2*3^2 divisible by 4
B. 2^2*3^2 not divisible by 8
C. 2^2*3^2 divisible by 9
D. 2^2*3^2 divisble by 12
so A, C and D
x/144=k (integer) 144=2^4*3^2
the minimum that x can be 2^4*3^2 (x not zero, as sq. root defined over positive numbers)
if minumum x=2^4*3^2; sq root x is 2^2 *3
3 sqrtx =2^2*3^2 at aleast.
A. 2^2*3^2 divisible by 4
B. 2^2*3^2 not divisible by 8
C. 2^2*3^2 divisible by 9
D. 2^2*3^2 divisble by 12
so A, C and D
I get all the options..
My working as under,
x is divisible by 144 => x is a multiple of 144, may be 144*n
3sqrt(x) = 3*sqrt(144*n) = 36sqrt(n).
Since, 36 is divisible by all the options given, I get all the options as answer.
Please correct my working.
Pranay
My working as under,
x is divisible by 144 => x is a multiple of 144, may be 144*n
3sqrt(x) = 3*sqrt(144*n) = 36sqrt(n).
Since, 36 is divisible by all the options given, I get all the options as answer.
Please correct my working.
Pranay
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except that 36 is not divisible by 8Pranay wrote:I get all the options..
My working as under,
x is divisible by 144 => x is a multiple of 144, may be 144*n
3sqrt(x) = 3*sqrt(144*n) = 36sqrt(n).
Since, 36 is divisible by all the options given, I get all the options as answer.
Please correct my working.
Pranay
Thanks Scoobydoo for correcting.scoobydooby wrote:except that 36 is not divisible by 8Pranay wrote:I get all the options..
My working as under,
x is divisible by 144 => x is a multiple of 144, may be 144*n
3sqrt(x) = 3*sqrt(144*n) = 36sqrt(n).
Since, 36 is divisible by all the options given, I get all the options as answer.
Please correct my working.
Pranay
That is the silliest mistake that one can make..
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