SOLUTION: Give an example of numbers a and b that show {{{sqrt(A + B)}}} is not the same as {{{sqrt(A) + sqrt(B)}}}

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Question 626114: Give an example of numbers a and b that show sqrt%28A+%2B+B%29 is not
the same as sqrt%28A%29+%2B+sqrt%28B%29
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
Give an example of numbers a and b that show sqrt%28A+%2B+B%29 is not
the same as sqrt%28A%29+%2B+sqrt%28B%29
Let A = 16, B = 9

sqrt%2816+%2B+9%29 = sqrt%2825%29 = 5

sqrt%2816%29 + sqrt%289%29 = 4 + 3 = 7

5 does not equal 7.

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Find all values of a and b that make those two expressions equal to each other.


sqrt%28A+%2B+B%29 = sqrt%28A%29+%2B+sqrt%28B%29

Square both sides of the equation:

%28sqrt%28A+%2B+B%29%29%5E2 = %28sqrt%28A%29+%2B+sqrt%28B%29%29%5E2

 A + B = A + 2sqrt%28A%29sqrt%28B%29 + B

Simplify the equation:

     0 = 2sqrt%28A%29sqrt%28B%29

Divide both sides by 2

     0 = sqrt%28A%29sqrt%28B%29

Square both sides

    0² = %28sqrt%28A%29sqrt%28B%29%29%5E2

     0 = AB

So it's only true if the product of A and B is zero.
That is to say, one or both of A and B must be equal 
to zero.
 
Edwin