a)(√15 +2√3)² +12√5 = 15 + 2. $\sqrt[]{15}$ . 2$\sqrt{3}$ + 12 +12√5
= 15+ 12√5 +12 + 12√5 = 27 + 24√5
b) ( √6 + 2)( √3 - √2 ) = $\sqrt{2}$ . ($\sqrt{3}$+$\sqrt{2}$) . ( $\sqrt{3}$-$\sqrt{2}$)
= $\sqrt{2}$ (3-2) = $\sqrt{2}$
c) (1 + √2 - √3)(1 + √2 + 3)
= 1 + √2 + 3 + √2 + 2 + 3√2 - √3 - √6 - 3√3
= 6 + 5√2 - 4√3 - √6
d) √3 ( √2 - √3)² - ( √3 + √2)
= √3 ( 2- 2√6 + 3) - (√3 + √2)
= 2√3 - 2√18 + 3√3 - √3 - √2
= 4√3 - 6√2 - √2 = 4√3 - 7√2