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

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Math Expert
Joined: 02 Sep 2009
Posts: 64158

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25 Apr 2017, 01:27
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$$\frac{5+5*\sqrt{5}}{10+\sqrt{500}}$$

A. 1/2

B. 2

C. $$1+\sqrt{5}$$

D. $$1+5\sqrt{5}$$

E. $$5+\sqrt{5}$$

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25 Apr 2017, 03:01
5+5*root(5) = 5 (1+root(5))
10+root(500) = 10 (1+root(5))

dividing them, we get 5/10 = 1/2

Hence, A will be the answer.
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25 Apr 2017, 03:08
Bunuel wrote:
$$\frac{5+5*\sqrt{5}}{10+\sqrt{500}}$$

A. 1/2

B. 2

C. $$1+\sqrt{5}$$

D. $$1+5\sqrt{5}$$

E. $$5+\sqrt{5}$$

Bunuel: the title shows that the denominator part is 5000^0.5 instead of 500^0.5. Could you please correct it ? Cheers
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Joined: 02 Sep 2009
Posts: 64158

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25 Apr 2017, 03:21
0akshay0 wrote:
Bunuel wrote:
$$\frac{5+5*\sqrt{5}}{10+\sqrt{500}}$$

A. 1/2

B. 2

C. $$1+\sqrt{5}$$

D. $$1+5\sqrt{5}$$

E. $$5+\sqrt{5}$$

Bunuel: the title shows that the denominator part is 5000^0.5 instead of 500^0.5. Could you please correct it ? Cheers

It's $$\sqrt{500}$$. Edited. Thank you.
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25 Apr 2017, 18:50
taking 5 common from numerator and 10 common from denominator we observe that the remaining factor will be 1+ $$\sqrt{5}$$ in both numerator and denominator. Canceling the common factor we see only $$\frac{5}{10}$$= $$\frac{1}{2}$$
Option A
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27 Apr 2017, 10:04
Eq 1 : 5+5* root 5 ---> 5 (1+root 5)
Eq 2 : 10+root 500 ---> 10 + root [5 * 10 * 10] ---> 10 + 10 root 5 ---> 10 (1+root 5)

Now, Eq 1/ Eq2 ----> 5(1 + root 5)/ 10 (1 + root 5) ---> 5/10 ---> 1/2

Hence ans : A
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28 Apr 2017, 14:12
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Bunuel wrote:
$$\frac{5+5*\sqrt{5}}{10+\sqrt{500}}$$

A. 1/2

B. 2

C. $$1+\sqrt{5}$$

D. $$1+5\sqrt{5}$$

E. $$5+\sqrt{5}$$

We can simplify √500 in the denominator: √500 = √100 x √5 = 10√5

Thus, the given expression becomes:

(5 + 5√5)/(10 + 10√5)

Pull out the common factor 2 from the expression in the denominator:

(5 + 5√5)/[2(5 + 5√5)]

1/2

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13 Mar 2020, 06:41
Bunuel wrote:
$$\frac{5+5*\sqrt{5}}{10+\sqrt{500}}$$

A. 1/2

B. 2

C. $$1+\sqrt{5}$$

D. $$1+5\sqrt{5}$$

E. $$5+\sqrt{5}$$

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

Or, $$\frac{5+5\sqrt{5}}{10+10\sqrt{5}}$$

Or, $$\frac{5 ( 1 + √5)}{10( 1 + √5)}=\frac{1}{2}$$, Answer must be (A)
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Re: (5+5*5^(1/2))/(10+500^(1/2))   [#permalink] 13 Mar 2020, 06:41