Question

Answer 1

b: \(=4\sqrt{2}-2\sqrt{6}+4\sqrt{3}-6-4\sqrt{3}+2\sqrt{6}-4\sqrt{2}\)

=-6

d: \(=8-2\sqrt{15}+2\sqrt{15}=8\)

Answer 2

\(b,=4\sqrt{2}+4\sqrt{3}-2\sqrt{6}-6-4\sqrt{3}+2\sqrt{6}-4\sqrt{2}=-6\\ d,=5-2\sqrt{15}+3+2\sqrt{15}=8\\ f,=3-4\sqrt{15}+20-4\left(3+2\sqrt{15}+5\right)=23-4\sqrt{15}-32-8\sqrt{15}=-9-12\sqrt{15}\)

Answer 3

`b)`\(\left(\sqrt{2}+\sqrt{3}\right)\left(4-2\sqrt{3}\right)-2\left(2\sqrt{3}-\sqrt{6}\right)-4\sqrt{2}\)

\(=4\sqrt{2}-2\sqrt{6}+4\sqrt{3}-6-4\sqrt{3}+2\sqrt{6}-4\sqrt{2}\)

\(=-6\)

`d)`\(\left(\sqrt{5}-\sqrt{3}\right)^2+2\sqrt{15}\)

\(=5+3-2\sqrt{15}+2\sqrt{15}\)

`=8`

`f)`\(\left(\sqrt{3}-2\sqrt{5}\right)^2-4\left(\sqrt{3}+\sqrt{5}\right)^2\)

\(=3+20-4\sqrt{15}-4\left(8+2\sqrt{15}\right)\)

\(=23-4\sqrt{15}-32-8\sqrt{15}\)

\(=-9-12\sqrt{15}\)