Question

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

b) \(\sqrt{7+4\sqrt{3}}-\sqrt{4+2\sqrt{3}}\)

c) \(\sqrt{8+2\sqrt{7}}+\sqrt{8-2\sqrt{7}}\)

d)\(\sqrt{7+2\sqrt{10}}-\sqrt{3-2\sqrt{2}}\)

Answer 1

a) \(=\sqrt{\left(\sqrt{5}-1\right)^2}-\sqrt{\left(\sqrt{5}+1\right)^2}=\sqrt{5}-1-\sqrt{5}-1=-2\)

b) \(=\sqrt{\left(2+\sqrt{3}\right)^2}-\sqrt{\left(1+\sqrt{3}\right)^2}=2+\sqrt{3}-1-\sqrt{3}=1\)

c) \(=\sqrt{\left(\sqrt{7}+1\right)^2}+\sqrt{\left(\sqrt{7}-1\right)^2}=\sqrt{7}+1+\sqrt{7}-1=2\sqrt{7}\)

d) \(=\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{2}-1\right)^2}=\sqrt{5}+\sqrt{2}-\sqrt{2}+1=\sqrt{5}+1\)