Asked by emily
Explain why sqrt(a+b) does not equal sqrt a + sqrt b, for a>0 and b>0?
Answers
Answered by
Steve
because
(a+b)^2 ≠ a^2 + b^2
sqrt is not a linear operator
(a+b)^2 ≠ a^2 + b^2
sqrt is not a linear operator
Answered by
Reiny
How about an indirect proof:
Assume that √(a+b) = √a + √b , for all a, b > 0
all we need is one counter-example to show my assumption is false:
is √(9 + 16) = √9 + √16 ???
LS = √25 = 5
RS = 3 + 4 = 7
RS ≠ LS
so I have a case where my assumption is false, all done
Assume that √(a+b) = √a + √b , for all a, b > 0
all we need is one counter-example to show my assumption is false:
is √(9 + 16) = √9 + √16 ???
LS = √25 = 5
RS = 3 + 4 = 7
RS ≠ LS
so I have a case where my assumption is false, all done
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