kamalkicks wrote:

if d is a positive integer, is \(\sqrt{d}\) an integer ?

a . \(\sqrt{9d}\) is an integer

b. \(\sqrt{10d}\) is not an integer.

is oa correct???????? if then please prove....

Original answer is correct.

A. \(\sqrt{9d}\) is an integer: tells us 3 \(sqrt d\) is an integer. therefore \(sqrt d\)has to be an integer. If it is not, we will never get an integer value. Sufficient.

B. \(\sqrt{10d}\) is not an integer:

Case 1: Assume D to be 4

Case 2: Assume D to be 6

In both cases, \(sqrt (10D)\) will not be an integer (satisfies the condition)

Now in case 1, \(sqrt D\) is an integer but in case 2, \(sqrt D\) is not an integer. 2 different answers satisfy the condition. Not sufficient.

Answer A.

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