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 = 8Plug these values into the equation to get: (
8)(√a - √b) =
16 From this, we can see that
√a - √b = 2We have:
√a + √b = 8√a - √b = 2When 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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