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[(5√3+3√5)/(√5+√3)]^2=?

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[(5√3+3√5)/(√5+√3)]^2=?  [#permalink]

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New post Updated on: 24 Nov 2016, 21:26
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

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\([(5√3+3√5)/(√5+√3)]^2\)=?

A. √6
B. √15
C. 15
D. √24
E. 6

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Originally posted by MathRevolution on 28 Sep 2016, 03:01.
Last edited by MathRevolution on 24 Nov 2016, 21:26, edited 3 times in total.
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Re: [(5√3+3√5)/(√5+√3)]^2=?  [#permalink]

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New post 28 Sep 2016, 03:24
MathRevolution wrote:
[(5√3+3√5)/(√5+√3)]2=?
A. √6 B. √15 C. 15 D. √24 E. 6


(5√3+3√5)/(√5+√3)]2=[(√5*√5*√3+√3*√3*√5)/(√5+√3)]*2= [(√5+√3)(√5*√3)/(√5+√3)]*2=2√15..
But looking at the answer, it seems it is not *2 but ^2..
So answer = (√15)^2=15..
C..

Request Mathrevolution, pl post Q correctly. Most of the time one has to work reverse..
Look at the OA and then correct Q accordingly
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Re: [(5√3+3√5)/(√5+√3)]^2=?  [#permalink]

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New post 28 Sep 2016, 03:47
chetan2u wrote:
MathRevolution wrote:
[(5√3+3√5)/(√5+√3)]2=?
A. √6 B. √15 C. 15 D. √24 E. 6


(5√3+3√5)/(√5+√3)]2=[(√5*√5*√3+√3*√3*√5)/(√5+√3)]*2= [(√5+√3)(√5*√3)/(√5+√3)]*2=2√15..
But looking at the answer, it seems it is not *2 but ^2..
So answer = (√15)^2=15..
C..

Request Mathrevolution, pl post Q correctly. Most of the time one has to work reverse..
Look at the OA and then correct Q accordingly


Exactly, did same calculation and got 2√15.

But based on that square at top the answer would be option C.
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Re: [(5√3+3√5)/(√5+√3)]^2=?  [#permalink]

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New post 28 Sep 2016, 06:57
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MathRevolution wrote:
[(5√3+3√5)/(√5+√3)]²=?
A. √6
B. √15
C. 15
D. √24
E. 6


[(5√3+3√5)/(√5+√3)
Square numerator and denominator to get: [75 + 15√15 + 15√15 + 45]/[5 + √15 + √15 + 3]
Simplify to get: [120 + 30√15]/[8 + 2√15]

NOTE: At this point, we COULD multiply top and bottom by the conjugate (8 - 2√15). HOWEVER, we can save time by recognizing that we can first factor the top and bottom.

Factor the top and bottom to get: [30(4 + √15)]/[2(4 + √15)]
Eliminate (4 + √15) from top and bottom to get: 30/2
Evaluate: 15

Answer:

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Re: [(5√3+3√5)/(√5+√3)]^2=?  [#permalink]

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New post 30 Sep 2016, 06:44
==> [(5√3+3√5)/(√5+√3)]2=[√15(√5+√3)/(√5+√3)]2=(√15)2=15 Hence the answer is C.
Answer: C
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Re: [(5√3+3√5)/(√5+√3)]^2=?  [#permalink]

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New post 22 Feb 2020, 08:51
\([(5√3+3√5)/(√5+√3)]^2\)=?

A. √6
B. √15
C. 15 --> correct: \( [(5√3+3√5)/(√5+√3)]^2= [(√5√3)(√5+√3)/(√5+√3)]^2 = (√5√3)^2 = 15\)
D. √24
E. 6
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Re: [(5√3+3√5)/(√5+√3)]^2=?   [#permalink] 22 Feb 2020, 08:51
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