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2. 82 (82)^(1/2) can't be written as an integer as 82 is not a perfect square .
3. ((82)^(1/2) * (82)^(1/2) )/82 = 1 Integer
Answer E
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Re: Which of the following expressions can be written as an integer?
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16 Oct 2015, 08:47
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1st:
[SQRT(82) + SQRT(82)]^2
we have formula (a+b)^2 = a^2 +b^2 +2ab we can rewrite the first statement as 82+82 + 2*[SQRT(82)*SQRT(82)] [SQRT(82)*SQRT(82)] this is equal to 82. we get an integer.
We can eliminate (A) None (C) III only
Statement II: 82*sqrt(82) we know that 82 is not a perfect square, thus, it is not an integer. Statement II will not yield an integer. We can eliminate:
(D) I and II
Statement III: [sqrt(82) * sqrt (82)]/82 sqrt(82) multiplied by itself will result in 82. 82 divide by 82, and get 1. This is an integer.
Eliminate answer choice B, and the only answer choice left, the correct one is E.
Re: Which of the following expressions can be written as an integer?
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17 Oct 2015, 11:56
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I. We use the identity (a+b)^2 = a^2+2ab+b^2 which gives us: 82 + (2*\(\sqrt{82}\)*\(\sqrt{82}\)) + 82 Since \(\sqrt{82}\)*\(\sqrt{82}\) equals 82 this will yield an integer.
II. No since \(\sqrt{82}\) is not a perfect square and you cannot separate it either into to two perfect squares.
III. Since \(\sqrt{82}\)*\(\sqrt{82}\) equals 82 this will yield an integer : 82/82=1
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Re: Which of the following expressions can be written as an integer?
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10 May 2016, 17:57
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Attached is a visual that should help.
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Screen Shot 2016-05-10 at 5.49.00 PM.png [ 153.51 KiB | Viewed 9031 times ]
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Re: Which of the following expressions can be written as an integer?
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11 Nov 2016, 14:00
lets see the options => Option 1=> (2√82)^2=> 4*82 => integer Option 2 => 82√82 => non integer Option 3 => √82*√82 / 82 => 82/82=> 1 , which is off course an integer. Hence E
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Re: Which of the following expressions can be written as an integer?
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11 Nov 2016, 14:59
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Bunuel wrote:
Which of the following expressions can be written as an integer?
I. \((\sqrt{82} + \sqrt{82})^2\)
II. \(82\sqrt{82}\)
III. \(\frac{\sqrt{82}\sqrt{82}}{82}\)
(A) None (B) I only (C) III only (D) I and II (E) I and III
We'll use the fact that (√82)(√82) = 82
I. (√82 + √82)² = (2√82)² = (2√82)(2√82) = (2)(2)(√82)(√82) = (4)(82) = some integer II. Doesn't look like it could be an integer. I'm not sure, so I'll move onto to statement III III. (√82)(√82)/82 = 82/82 = 1
NOTE: As we check each statement, we should also check the answer choices. Since I and III both work, the correct answer must be E, since there's no option for all 3 to be true.
Re: Which of the following expressions can be written as an integer?
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23 Mar 2017, 23:16
i. \({ \left( \sqrt { 82 } +\sqrt { 82 } \right) }^{ 2 }=\left( 2\sqrt { 82 } \right) ^{ 2 }\Rightarrow\) At this moment you already know you have an integer without further calculations.
ii. \(82\sqrt { 82 } \Rightarrow\) We also know that perfect squares don't end in 2, 3, 7 or 8. So, rule this one out as this product won't yield an integer.
Re: Which of the following expressions can be written as an integer?
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20 Jun 2018, 03:08
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