Simplify each of the following expressions:
(i) (3+√3)(2+√2)
(ii) (3+√3)(3−√3)
(iii) (√5+√2)²
(iv) (√5−√2)(√5+√2)

We know that, (A+B)(C+D) = A×(C+D) + B×(C+D) = AC+AD+BC+CD
(i) (3+√3)(2+√2) = (6+2√3+3√2+√6)
(ii) (√5+√2)² = (√5)² + 2(√5)(√2) + (√2)² = 5 + 2√10 + 2 = 7 + 2√10
(iii) (3+√3)(3−√3) = (3)² − (√3)² = 9 − 3 = 6
(iv) (√5−√2)(√5+√2) = (√5)² − (√2)² = 5 − 2 = 3