Question

a) \(\sqrt{5+2\sqrt{6}}-\sqrt{3-2\sqrt{2}}\)

b) \(\sqrt{11+6\sqrt{2}}-\sqrt{18+8\sqrt{2}}\)

c) \(\sqrt{2}\sqrt{2-\sqrt{3}}\left(\sqrt{3}+1\right)\)

Answer 1

a)
\(\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{2}-1\right)^2}=\sqrt{3}+\sqrt{2}-\sqrt{2}+1=\sqrt{3}+1\)
b)
\(\sqrt{\left(\sqrt{9}+\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{16}+\sqrt{2}\right)^2}=\sqrt{9}+\sqrt{2}-\sqrt{16}-\sqrt{2}=3-4=-1\)
c)
\(=\sqrt{2\left(2-\sqrt{3}\right)}\left(\sqrt{3}+1\right)=\sqrt{\left(\sqrt{3}-1\right)^2}\left(\sqrt{3}+1\right)=\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)=3-1=2\)