Question

Answer 1

a: \(=\dfrac{12\left(3+\sqrt{3}\right)}{6}=2\left(3+\sqrt{3}\right)=6+3\sqrt{3}\)

b: \(=\dfrac{8\left(\sqrt{5}-2\right)}{1}=8\sqrt{5}-16\)

c: \(=\dfrac{14\left(\sqrt{10}-\sqrt{3}\right)}{7}=2\left(\sqrt{10}-\sqrt{3}\right)\)

d: \(=\dfrac{\left(7\sqrt{3}-5\sqrt{11}\right)\left(8\sqrt{3}+7\sqrt{11}\right)}{192-539}\)

\(=\dfrac{168+49\sqrt{33}-40\sqrt{33}-385}{-347}\)

\(=\dfrac{-217+9\sqrt{33}}{-347}=\dfrac{217-9\sqrt{33}}{347}\)

e: \(=\dfrac{\left(3\sqrt{5}-2\sqrt{2}\right)\left(2\sqrt{5}+3\sqrt{2}\right)}{2}\)

\(=\dfrac{30+9\sqrt{10}-4\sqrt{10}-12}{2}=\dfrac{18-5\sqrt{10}}{2}\)