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(5 + 5√5)/(10 + √500)

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(5 + 5√5)/(10 + √500) [#permalink]

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New post 23 Sep 2015, 01:38
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

89% (00:49) correct 11% (01:45) wrong based on 83 sessions

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Re: (5 + 5√5)/(10 + √500) [#permalink]

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New post 23 Sep 2015, 01:50
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Answer is A.

5(1+root5)/10(1+root5) which equals 1/2

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Re: (5 + 5√5)/(10 + √500) [#permalink]

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New post 23 Sep 2015, 02:42
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Bunuel wrote:
\(\frac{5 + 5\sqrt{5}}{10+\sqrt{500}}=\)

A) 1/2
B) 2
C) 1 + √5
D) 1 + 5√5
E) 5 + √5

Kudos for a correct solution.


numerator: [5 + 5(5)^1/2] X [5 - 5(5)^1/2]
denominator: [10 + (500)^1/2] x [5 - 5(5)^1/2]

numerator = 25 -5x5x5 = -100
denominator = 50 - 5x5x10 = -200

numerator/denominator = -100/-200 = 1/2

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(5 + 5√5)/(10 + √500) [#permalink]

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New post 23 Sep 2015, 02:57
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Answer A:

(5+5√5)/(10+√500)

=(5+5√5)/(10+√5³*2²)

=(5+5√5)/(10+5*2√5)

=(5+5√5)/(10+10√5)

=(5(1+√5))/(10(1+√5))

=5/10 = 1/2

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(5 + 5√5)/(10 + √500) [#permalink]

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New post 23 Sep 2015, 04:24
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Bunuel wrote:
\(\frac{5 + 5\sqrt{5}}{10+\sqrt{500}}=\)

A) 1/2
B) 2
C) 1 + √5
D) 1 + 5√5
E) 5 + √5

Kudos for a correct solution.


\(\frac{5 + 5\sqrt{5}}{10+\sqrt{500}}\)

=\(\frac{5 + 5\sqrt{5}}{10+10\sqrt{5}}\)

=\(\frac{5(1 + \sqrt{5})}{10(1+\sqrt{5})}\)

=\(\frac{5}{10}\)

=\(\frac{1}{2}\)

Answer:- A

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Re: (5 + 5√5)/(10 + √500) [#permalink]

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New post 23 Sep 2015, 05:26
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I struggled on solving so I used trick :

1st - convert the square root of 500 in decent form : (5 + 5√5)/(10 + 10√5)
2nd - Factorise 5 in numerator and denominator : 5*(1+√5) / 5*(2+2√5)

You end up with the following expression : 1+√5 / 2+2√5

Now if you look at the answer choices, there's only one that holds value between 0 and 1 (1/2-answer A).

Looking again at the expression, you can see that it cannot be above 1, so answer A it is.

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Re: (5 + 5√5)/(10 + √500) [#permalink]

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New post 23 Sep 2015, 06:05
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Toutatis wrote:
I struggled on solving so I used trick :

1st - convert the square root of 500 in decent form : (5 + 5√5)/(10 + 10√5)
2nd - Factorise 5 in numerator and denominator : 5*(1+√5) / 5*(2+2√5)

You end up with the following expression : 1+√5 / 2+2√5

Now if you look at the answer choices, there's only one that holds value between 0 and 1 (1/2-answer A).

Looking again at the expression, you can see that it cannot be above 1, so answer A it is.


If you have: \(\frac{5 + 5√5}{10 + 10√5}\), you can factorise:
Numerator: \(1*(5 + 5√5)\)
Denominator: \(2*(5 + 5√5)\).

So you have \(\frac{1*(5 + 5√5)}{2*(5 + 5√5)}\) \(=\frac{1}{2}\)

Hope it helps.
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Re: (5 + 5√5)/(10 + √500) [#permalink]

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New post 24 Sep 2015, 07:15
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Answer : 1/2 (A)

5 (1+ root5) / 10 (1+ root5) = 5/10 = 1/2 (A)

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Re: (5 + 5√5)/(10 + √500) [#permalink]

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New post 24 Sep 2015, 08:31
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I believe the answer is A. See below for explanation.

(5 + 5√5) / (10 + √500)
5(1+√5) / 10(1+√5)
5/10*(1+√5)/(1+√5)
1/2*1
1/2

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Re: (5 + 5√5)/(10 + √500) [#permalink]

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Re: (5 + 5√5)/(10 + √500)   [#permalink] 27 Oct 2017, 21:47
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