Question

What is the following product?

(5 StartRoot 2 EndRoot minus 4 StartRoot 3 EndRoot) (5 StartRoot 2 EndRoot minus 4 StartRoot 3 EndRoot)
–2
2
22 – 40 StartRoot 6 EndRoot
98 – 41 StartRoot 6 EndRoot

Answer 1

There are two plausible interpretations:

1) If both factors are the same, (5√2 − 4√3)^2:
(5√2)^2 + 2(5√2)(−4√3) + (−4√3)^2 = 50 − 40√6 + 48 = 98 − 40√6.

2) If the factors are conjugates, (5√2 − 4√3)(5√2 + 4√3) = (5√2)^2 − (4√3)^2 = 50 − 48 = 2.

So the product is 98 − 40√6 in the “square” case, and 2 in the “conjugate” case.