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If a – b = 16 and

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If a – b = 16 and [#permalink] New post 21 Jun 2017, 13:41
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If a – b = 16 and \(\sqrt{a} + \sqrt{b} = 8\) , what is the value \(\sqrt{ab}\) ?

(A) 2
(B) 4
(C) 8
(D) 12
(E) 15
[Reveal] Spoiler: OA

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Re: If a – b = 16 and [#permalink] New post 25 Jul 2017, 07:59
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Carcass wrote:


If a – b = 16 and \(\sqrt{a} + \sqrt{b} = 8\) , what is the value \(\sqrt{ab}\) ?

(A) 2
(B) 4
(C) 8
(D) 12
(E) 15


IMPORTANT: (√a + √b)(√a - √b) = a - b [this is a cute version of difference of squares]
We're told that a - b = 16 AND √a + √b = 8
Plug these values into the equation to get: (8)(√a - √b) = 16
From this, we can see that √a - √b = 2

We have:
√a + √b = 8
√a - √b = 2

When we ADD the two equations, we get: 2√a = 10, which means √a = 5
When we SUBTRACT the bottom equation from the top, we get: 2√b = 6, which means √b = 3

So, √(ab) = (√a)(√b) = (5)(3) = 15

Answer: E

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Re: If a – b = 16 and [#permalink] New post 25 Jul 2017, 23:45
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Hi! great question. Are there any more like this? Request you to see if its possible to post it here! Thank you
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Re: If a – b = 16 and [#permalink] New post 26 Jul 2017, 04:27
Expert's post
greprepclub-the-questions-vault-3523.html#p7347

More questions on their way

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Re: If a – b = 16 and [#permalink] New post 23 Nov 2017, 22:59
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I am posting my answer to exemplify how important it is to make sure you are taking the shortest possible route when solving a problem. I didn't do that and look at the monster I got when I tried to use substitution:

A - B = 16
A = 16 + B

Now I substituted the A for 16 + B in the other equation:

√A + √B) = 8
√(16 + B) + √B = 8

√(16 + B) = 8 - √B

Both sides are squared trying to get rid of the square root:

(√(16 + B))^2 = (8 - √B)^2
16 + B = (8 - √B) x (8 - √B)
16 + B = 64 -16√B + B
-64 -B -64 -B
-48 = -16√B

Square both sides again to get rid of the radical:

(-48)^2 = (-16√B)^2
2304 = 256B
B = 2304/256
B = 9

Now substitute the B in the first equation:

A - B = 16
A - 9 = 16
A = 25

Now plug in A and B in the third equation:

√AB = ?
√(9) x (25)
√225
= 15

Sorry it is a little confusing. This is my first post. I am a little pround I got the final result after this mathmatical ordeal.
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Re: If a – b = 16 and [#permalink] New post 03 Nov 2018, 12:14
Once you hit the right road, its real easy.

a - b = (root(a) + root(b)) (root(a) - root(b))
Re: If a – b = 16 and   [#permalink] 03 Nov 2018, 12:14
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