Discussion
If x and y are perfect squares, then which of the following is not necessarily a perfect square?
| (A) | x2 |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 09/16/2012 22:22
Can you also explain why E) isn't correct?
Posted: 12/17/2012 21:11
X^5 is also not a perfect square
Posted: 12/17/2012 22:08
Hi there. The keywords are "not necessarily". So if x^5 can be a perfect square, even if sometimes it is not a perfect square, then it is not the choice. For example, if x is 4, 4^5 is 1024, which is a perfect square of 32.
Posted: 01/29/2013 19:48
I am sorry, this confuses me, the question asks for one which is "not necessarily a perfect square" which means that the correct answer can at times be a perfect square and at other times not a perfect square; meaning (e) which can be a perfect square but can also not be a perfect square would be an appropriate answer right? Similarly with (x•y) where if we choose 4•16=54 which is not a perfect square but if we choose 4•9=36 then it is a perfect square, which again satisfies the "not necessarily" criteria...
Posted: 01/29/2013 23:51
Robert, the first explanation was not very good. The right way to answer this question is to ask: if we take the square root, will we get a whole number? Since x and y are perfect squares, we can see that the square root of answer choices ABCE will be whole, since they involve products of perfect
squares. Answer choice D however involves the sum of two perfect squares, and if we take the sqrt, the outcome is not necessarily a whole number. Btw, 4x16 is 64, which is a perfect square, not 54.
squares. Answer choice D however involves the sum of two perfect squares, and if we take the sqrt, the outcome is not necessarily a whole number. Btw, 4x16 is 64, which is a perfect square, not 54.
Posted: 08/15/2013 13:36
How about 9+16=25?X+Y can be perfect square.
Posted: 08/15/2013 17:20
Echo, pay attention to "not necessarily".
Posted: 09/09/2013 07:37
Hi，so "not necessarily" here means it can be a perfect square and it can also be a non perfect square? It depends, right? Thanks
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Edit
Posted: 09/13/2013 16:19
Yue Meng, yes.
Posted: 12/23/2013 13:50
This question is confusing because it would lead one to believe that the ones which would turn out to not be a perfect square all the time would be the answer.... can you explain?
Posted: 12/23/2013 20:45
Mycal, this was explained before in the read so let me post again: the first explanation was not very good. The right way to answer this question is to ask: if we take the square root of the answers, will we get a whole number? Since x and y are perfect squares, we can see that the square root of answer choices ABCE will be whole, since they involve products of perfect squares. Let x = z^2, z is an integer, which means that x is a perfect square (of z). x^5 is z^10, and sqrt(z^10) is z^5, which is a whole number. E is always a perfect square.
Posted: 10/21/2014 22:17
Where do you get numbers 4 and 9?
Posted: 10/21/2014 22:38
Chris, 4 and 9 are perfect squares of 2 and 3. We just use them to test the statements / choices, because they are easy to work with. We could have picked 625 or 1025, but they would be more difficult to work with.
Posted: 01/07/2015 03:54
What's the perfect square ?
Posted: 05/22/2015 13:42
A perfect square is a square number, like 4, 9,16, 25, 36 ...
Posted: 02/10/2015 07:37
How do you know to chose 4 & 9?
Posted: 05/22/2015 13:41
Kathy, you start with the simplest numbers, like 2 or 3, for plugging in, because they are the easiest to work with.