Question 626114
Give an example of numbers a and b that show {{{sqrt(A + B)}}} is not 
the same as {{{sqrt(A) + sqrt(B)}}}
<pre>
Let A = 16, B = 9

{{{sqrt(16 + 9)}}} = {{{sqrt(25)}}} = 5

{{{sqrt(16)}}} + {{{sqrt(9)}}} = 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(A + B)}}} = {{{sqrt(A) + sqrt(B)}}}

Square both sides of the equation:

{{{(sqrt(A + B))^2}}} = {{{(sqrt(A) + sqrt(B))^2}}}

 A + B = A + 2{{{sqrt(A)sqrt(B)}}} + B

Simplify the equation:

     0 = 2{{{sqrt(A)sqrt(B)}}}

Divide both sides by 2

     0 = {{{sqrt(A)sqrt(B)}}}

Square both sides

    0² = {{{(sqrt(A)sqrt(B))^2}}}

     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</pre>