Question

Tính

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

b) \(\sqrt{9-4\sqrt{5}}+\sqrt{6+2\sqrt{5}}\)

Answer 1

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

= \(\sqrt{2-2\sqrt{2}+1}\)+ \(\sqrt{2+2\sqrt{2}+1}\)

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

= \(\sqrt{2}\)-1+\(\sqrt{2}\)+1

=2\(\sqrt{2}\)

b) \(\sqrt{9-4\sqrt{5}}\)+ \(\sqrt{6+2\sqrt{5}}\)

= \(\sqrt{4-4\sqrt{5}+5}\)+\(\sqrt{4+2\sqrt{5}+2}\)

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

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

= 4-\(\sqrt{5}\)+\(\sqrt{2}\)