\((\sqrt[4]{3} + \sqrt[4]{2})(\sqrt[4]{3} - \sqrt[4]{2})(\sqrt{3} + \sqrt{2})\) is equal to
A
1
B
(\(\sqrt{2} + 4\sqrt{2}\))
C
(6\(\sqrt{2}\)
D
8
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\((\sqrt[4]{3} + \sqrt[4]{2})(\sqrt[4]{3} - \sqrt[4]{2})(\sqrt{3} + \sqrt{2})\)
\((\sqrt[4]{3} + \sqrt[4]{2})(\sqrt[4]{3} - \sqrt[4]{2}) = \sqrt{3} - \sqrt[4]{6} + \sqrt[4]{6} - \sqrt{2}\)
= \(\sqrt{3} - \sqrt{2}\)
\((\sqrt{3} - \sqrt{2})(\sqrt{3} + \sqrt{2}) = 3 + \sqrt{6} - \sqrt{6} - 2\)
= \(3 - 2 = 1\)
Source: Myschool Past Questions Archive (Record #32221)