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If a - b = 16

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If a - b = 16 [#permalink]  19 Aug 2017, 04:41
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85% (01:01) correct 14% (00:00) wrong based on 7 sessions
If $$a - b = 16$$ and $$\sqrt{a} + \sqrt{b} = 8$$, what is the value of $$\sqrt{ab}$$ ?

A. 2

B. 4

C. 8

D. 12

E. 15

Hello!

I have the answer to this question in my book using other methods. However, whenever I try to solve this question using the substitution method, my solution is not the same as what my book says. Would you please be kind enough to solve this question for me using the SUBSTITUTION method?

I know there are easier methods as well but I need to know what mistake I am making by using the substitution method.
[Reveal] Spoiler: OA

Last edited by Carcass on 19 Aug 2017, 07:46, edited 1 time in total.
Edited by Carcass
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Re: If a - b = 16 [#permalink]  19 Aug 2017, 07:47
Expert's post
Please follow the rules. Do not post a screenshot of a question. But text it.

Thank you so much.

Regards
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Re: If a - b = 16 [#permalink]  20 Aug 2017, 01:42
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but for substitution method it should be mentioned that a and b are integers:

Keeping this in mind write all the numbers which sums equal to 8 i.e 1+7,2+6,3+5,4+4
Now look for the difference of squares which is equal to 16 , 25-9 = 16.
Numbers are 25,9 so the ans is 15
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Re: If a - b = 16 [#permalink]  23 Aug 2017, 01:44
avdesh0490 wrote:
but for substitution method it should be mentioned that a and b are integers:

Keeping this in mind write all the numbers which sums equal to 8 i.e 1+7,2+6,3+5,4+4
Now look for the difference of squares which is equal to 16 , 25-9 = 16.
Numbers are 25,9 so the ans is 15

I didn't notice this. Can you write down your explanation thoroughly?
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Re: If a - b = 16 [#permalink]  04 Jun 2019, 07:21
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a and b are perfect squares as the addition of their square roots equal to an integer (8). In this case, only a=25 and b=9 match the conditions. So, answer is 15 ( after some calculation, right ?
Re: If a - b = 16   [#permalink] 04 Jun 2019, 07:21
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