The root of 8 plus the root of two is the same as the root of 8 plus 2. Which is the same as the root of 10. Since the power is 2 (applied to everything in the radicand) and the index is 2, this reduces to the power of 1 and the radical sign is disappears. What tracy did wrong was to multiply 2 and 8 when there was very clearly a plus sign there.
You said The root of 8 plus the root of two is the same as the root of 8 plus 2
Which is ******** .
a^(1/2)+b^(1/2)≠(a+b)^(1/2)
Example assuming a and b is equal to 4
4^(1/2)+4^(1/2)=4
(4+4)^(1/2)=2*2^(1/2)=2,828
4≠2,828
As you can see the statement that you made first is wrong.
And again you make the assumption that (a^(1/2)+b^(1/2))^2=a+b, which is false.
Example assuming a and b is equal to 2.
(2^(1/2)+2^(1/2))^2=8
2+2=4
8≠4
Trazy did not multiply 8 with 2.
The statement tracy made was that if you square an irrational number, you allways get a rational number, which is false
Example with the irrational number e, e≈2,71828128....
e^2≈7,39056...
e^2 is an irrational number, and that is where tracy was wrong, and not in the result of the calculation.
