Question

Answer 1

a) \(\sqrt{12-2\sqrt{35}}-\sqrt{12+2\sqrt{35}}=\sqrt{\left(\sqrt{7}-\sqrt{5}\right)^2}-\sqrt{\left(\sqrt{7}+\sqrt{5}\right)^2}=\sqrt{7}-\sqrt{5}-\sqrt{7}-\sqrt{5}=-2\sqrt{5}\)

b) \(=\sqrt{\left(\sqrt{7}+\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}=\sqrt{7}+\sqrt{3}-\sqrt{7}+\sqrt{3}=2\sqrt{3}\)

c) \(=\sqrt{\left(\sqrt{7}-\sqrt{5}\right)^2}-\sqrt{\left(\sqrt{7}+\sqrt{5}\right)^2}=\sqrt{7}-\sqrt{5}-\sqrt{7}-\sqrt{5}=-2\sqrt{5}\)

d) \(=\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}=\sqrt{5}+\sqrt{2}+\sqrt{5}-\sqrt{2}=2\sqrt{5}\)

e) \(=\sqrt{\left(\sqrt{7}-\sqrt{6}\right)^2}-\sqrt{\left(\sqrt{7}-\sqrt{6}\right)^2}=\sqrt{7}-\sqrt{6}-\sqrt{7}+\sqrt{6}=0\)