If Tracey is talking about the entire set of irrational numbers, then she is wrong, because cube roots, and 4th roots, etc are also irrational. Square root irrationals are a very small set of the total set of irrational numbers.
Sticking with just square roots, Tracey is also wrong because throw (sqrt(2) + sqrt(5))^2 and nope, still irrational. The only reason (sqrt(2) + sqrt(8)) works is because 2 x 8=16 and is a perfect square. 2 x 5=10, and will still be irrational, 2 x 6, 2 x 10, etc. all are still irrational.
The expansion of (A + B)^2 = A^2 + 2AB + B^2 in the 2 and 8 example, 2AB = 2 x sqrt(16) = 8. Change 2 or 8 to a set of numbers that when multiplied do not end up as a perfect square, and the answer will still have a sqrt in it - such as 2 and 5, or 2 and 6, etc.
[ + ] Prairie
[ - ] Prairie 1 point 2.9 yearsJul 1, 2022 08:22:03 ago (+1/-0)
[ + ] GrayDragon
[ - ] GrayDragon [op] 0 points 2.9 yearsJul 1, 2022 09:12:44 ago (+0/-0)
I don't know what ( (2^-1/2)^-1/2 + (2^-1/2)^-1/2 )^2 is, but you seem to be on the right path. I was thinking decimals.
Maybe Tracey isn't so stupid after all, haha!
[ + ] localsal
[ - ] localsal 0 points 2.9 yearsJul 1, 2022 14:08:43 ago (+0/-0)
Sticking with just square roots, Tracey is also wrong because throw (sqrt(2) + sqrt(5))^2 and nope, still irrational.
The only reason (sqrt(2) + sqrt(8)) works is because 2 x 8=16 and is a perfect square. 2 x 5=10, and will still be irrational, 2 x 6, 2 x 10, etc. all are still irrational.
The expansion of (A + B)^2 = A^2 + 2AB + B^2
in the 2 and 8 example, 2AB = 2 x sqrt(16) = 8. Change 2 or 8 to a set of numbers that when multiplied do not end up as a perfect square, and the answer will still have a sqrt in it - such as 2 and 5, or 2 and 6, etc.
[ + ] Prairie
[ - ] Prairie 0 points 2.9 yearsJul 2, 2022 07:19:32 ago (+0/-0)
[ + ] big_fat_dangus
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[ + ] PostWallHelena
[ - ] PostWallHelena 0 points 2.9 yearsJul 1, 2022 09:19:55 ago (+0/-0)
[ + ] big_fat_dangus
[ - ] big_fat_dangus 0 points 2.9 yearsJul 1, 2022 09:28:32 ago (+0/-0)
[ + ] PostWallHelena
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[ + ] big_fat_dangus
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[ + ] wonderfuldonut
[ - ] wonderfuldonut 1 point 2.9 yearsJul 1, 2022 05:36:50 ago (+1/-0)