SOLUTION: (square root 13 + square root z) (square root 13 - square root z)

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Question 130155: (square root 13 + square root z) (square root 13 - square root z)
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Throughout this problem, keep in mind that z%3E=0 (remember you cannot take the square root of a negative number)

%28sqrt%28+13%29+%2B+sqrt%28+z%29%29+%28sqrt%28+13%29+-+sqrt%28+z%29%29+ Start with the given expression


Foil the expression


sqrt%28+13%5E2%29-sqrt%28+13z%29%2Bsqrt%2813z%29-sqrt%28+z%5E2%29 Combine the roots


sqrt%28+13%5E2%29%2Bcross%28-sqrt%28+13z%29%2Bsqrt%2813z%29%29-sqrt%28+z%5E2%29 Cancel like terms


sqrt%28+13%5E2%29-sqrt%28+z%5E2%29 Simplify


13-z Take the square root of 13%5E2 to get 13. Take the square root of z%5E2 to get z.


So %28sqrt%28+13%29+%2B+sqrt%28+z%29%29+%28sqrt%28+13%29+-+sqrt%28+z%29%29+ simplifies to 13-z


In other words, %28sqrt%28+13%29+%2B+sqrt%28+z%29%29+%28sqrt%28+13%29+-+sqrt%28+z%29%29+=13-z

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(square root 13 + square root z) (square root 13 - square root z)
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this follows the form (a+b)(a-b) = a^2-b^2
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Your problem:
= 13 -z
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Cheers,
Stan H.