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(5 + 5√5)/(10 + √500)

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Math Expert
Joined: 02 Sep 2009
Posts: 64249
(5 + 5√5)/(10 + √500)  [#permalink]

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23 Sep 2015, 01:38
1
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Difficulty:

5% (low)

Question Stats:

94% (01:15) correct 6% (01:46) wrong based on 102 sessions

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$$\frac{5 + 5\sqrt{5}}{10+\sqrt{500}}=$$

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

Kudos for a correct solution.

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Joined: 02 Jan 2014
Posts: 35
Re: (5 + 5√5)/(10 + √500)  [#permalink]

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23 Sep 2015, 01:50
1

5(1+root5)/10(1+root5) which equals 1/2
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Joined: 27 Jun 2015
Posts: 6
Concentration: Marketing, Entrepreneurship
Schools: Haas '18
Re: (5 + 5√5)/(10 + √500)  [#permalink]

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23 Sep 2015, 02:42
1
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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Joined: 22 Sep 2015
Posts: 5
(5 + 5√5)/(10 + √500)  [#permalink]

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23 Sep 2015, 02:57
1

(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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Joined: 29 Jul 2015
Posts: 150
(5 + 5√5)/(10 + √500)  [#permalink]

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23 Sep 2015, 04:24
2
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.

$$\frac{5 + 5\sqrt{5}}{10+\sqrt{500}}$$

=$$\frac{5 + 5\sqrt{5}}{10+10\sqrt{5}}$$

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

=$$\frac{5}{10}$$

=$$\frac{1}{2}$$

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Joined: 08 Sep 2015
Posts: 1
Re: (5 + 5√5)/(10 + √500)  [#permalink]

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23 Sep 2015, 05:26
1
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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Joined: 02 Feb 2014
Posts: 36
Concentration: Finance, General Management
GPA: 3.5
Re: (5 + 5√5)/(10 + √500)  [#permalink]

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23 Sep 2015, 06:05
1
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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Joined: 03 May 2015
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Re: (5 + 5√5)/(10 + √500)  [#permalink]

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24 Sep 2015, 07:15
1

5 (1+ root5) / 10 (1+ root5) = 5/10 = 1/2 (A)
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Joined: 22 Aug 2012
Posts: 73
Concentration: Technology
GMAT 1: 710 Q47 V40
Re: (5 + 5√5)/(10 + √500)  [#permalink]

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24 Sep 2015, 08:31
1
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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27 Oct 2017, 21:47
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Re: (5 + 5√5)/(10 + √500)   [#permalink] 27 Oct 2017, 21:47