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If n is the square of a positive integer, which of the following must
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09 Nov 2015, 21:59
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Re: If n is the square of a positive integer, which of the following must
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10 Nov 2015, 00:53
Let a= +ve integer such that n= a^2 (a+1)= next +ve integer (a+1)^2 = a^2 + 1 + 2a and a=n^(1/2) Therefore , (a+1)^2=n+1+2*n^(1/2) Answer D Alternatively, we can take values let n= 4 =a^2 => a= 2 (a+1)=3^2 = 9 now checking the choices A. âˆšn + 1 = 2+1 =3 B. n + 1 = 4+1 =5 C. n^2 + 1 = 16+1 =17 D. n + 2âˆšn + 1 = 4+ 2*2 +1 = 9 Answer D E. n^2 + 2n + 1 = 16+ 8 + 1 =25
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Re: If n is the square of a positive integer, which of the following must
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10 Nov 2015, 10:26
If n is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
n = (x)^2 where x is a positive integer To calculate  (x+1)^2 = x^2 + 2x + 1 root(n) = x
Ans  n + 2 root(n) + 1 This should be D



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Re: If n is the square of a positive integer, which of the following must
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08 Oct 2016, 13:59
Bunuel wrote: If n is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
A. âˆšn + 1 B. n + 1 C. n^2 + 1 D. n + 2âˆšn + 1 E. n^2 + 2n + 1 next positive integer is sqrt(n)+1. square of this number is [sqrt(n)+1]^2 the result is definitely a number with an "n" not squared not under radical A,C, E out B can't be the answer so it must be D. not even needed to square everything...



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Re: If n is the square of a positive integer, which of the following must
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16 Oct 2016, 13:43
Bunuel wrote: If n is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
A. âˆšn + 1 B. n + 1 C. n^2 + 1 D. n + 2âˆšn + 1 E. n^2 + 2n + 1 n is +ve integer n = x^2 thus sqrt n = x , (x+1)^2 = x^2 + 2x+1 , substitute n^2+2sqrtn+1



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Re: If n is the square of a positive integer, which of the following must
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16 Oct 2016, 22:45
Bunuel wrote: If n is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
A. âˆšn + 1 B. n + 1 C. n^2 + 1 D. n + 2âˆšn + 1 E. n^2 + 2n + 1 Plug in some value and check  Let n = 1 ( least number ) Square of the next positive integer is 4 Now, check the options : Only (D) and (E) satisfies Check using one more square number to confirm the answerLet n = 4 ( least number ) Square of the next positive integer is 9 Now, check the options : Only (D) satisfies Hence answer must be option (D)
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Re: If n is the square of a positive integer, which of the following must
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13 Apr 2017, 03:43
Option D\(n = K^2\); K>0 and Integer \((K+1)^2 = K^2 + 2K + 1 = n + 2\sqrt{n} + 1\)
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If n is the square of a positive integer, which of the following must
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26 May 2017, 08:37
Skywalker18 wrote: Let a= +ve integer such that n= a^2 (a+1)= next +ve integer (a+1)^2 = a^2 + 1 + 2a
and a=n^(1/2) Therefore , (a+1)^2=n+1+2*n^(1/2) Answer D
Alternatively, we can take values let n= 4 =a^2 => a= 2 (a+1)=3^2 = 9 now checking the choices A. âˆšn + 1 = 2+1 =3 B. n + 1 = 4+1 =5 C. n^2 + 1 = 16+1 =17 D. n + 2âˆšn + 1 = 4+ 2*2 +1 = 9 Answer D E. n^2 + 2n + 1 = 16+ 8 + 1 =25 This question makes no sense to me . Isn't 5 the next positive integer after 4, and 5^2=25. I definitely did everything you prescribed on my first attempt at this question. Could you elaborate . Answer seems like it should be E to me . It always give you the square of the next positive integer . I am completely perplexed here. Think I'm just being dumb. Thanks !



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Re: If n is the square of a positive integer, which of the following must
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26 May 2017, 08:48
NanaA wrote: Skywalker18 wrote: Let a= +ve integer such that n= a^2 (a+1)= next +ve integer (a+1)^2 = a^2 + 1 + 2a
and a=n^(1/2) Therefore , (a+1)^2=n+1+2*n^(1/2) Answer D
Alternatively, we can take values let n= 4 =a^2 => a= 2 (a+1)=3^2 = 9 now checking the choices A. âˆšn + 1 = 2+1 =3 B. n + 1 = 4+1 =5 C. n^2 + 1 = 16+1 =17 D. n + 2âˆšn + 1 = 4+ 2*2 +1 = 9 Answer D E. n^2 + 2n + 1 = 16+ 8 + 1 =25 This question makes no sense to me . Isn't 6 the next positive integer after 4, and 6^2=36. I definitely did everything you prescribed on my first attempt at this question. Could you elaborate . Think I'm just being dumb. Thanks ! If n is the square of a positive integer, which of the following must be equal to the square of the next positive integer?A. \(\sqrt{n} + 1\) B. \(n + 1\) C. \(n^2 + 1\) D. \(n + 2\sqrt{n} + 1\) E. \(n^2 + 2n + 1\) n is the square of a positive integer. Say that positive integer is x. So, we are given that \(n = x^2\). Notice that from this it follows that \(x=\sqrt{n}\) Which of the following must be equal to the square of the next positive integer? The next positive integer is x + 1. Its square = \((x+1)^2=x^2+2x+1\). Substitute the values of x^2 and x from above to get: \((x+1)^2=x^2+2x+1=n+2\sqrt{n}+1\). Answer: D.
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Re: If n is the square of a positive integer, which of the following must
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17 Jul 2018, 15:45
Bunuel wrote: If n is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
A. \(\sqrt{n} + 1\)
B. \(n + 1\)
C. \(n^2 + 1\)
D. \(n + 2\sqrt{n} + 1\)
E. \(n^2 + 2n + 1\) We can let n = k^2 where k is a positive integer, we see that the square of the next positive integer is (k + 1)^2 = k^2 + 2k + 1. Since n = k^2, so k = âˆšn. Therefore, in terms of n, the square of the next positive integer is n + 2âˆšn + 1. Answer: D
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