Question

Thu gọn 

a, \(\sqrt{9-4\sqrt{5}}+\sqrt{9+4\sqrt{5}}\)

b, \(\sqrt{11+4\sqrt{6}}-\sqrt{11-4\sqrt{6}}\)

c, \(\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}\)

Answer 1

a) \(\sqrt{9-4\sqrt{5}}+\sqrt{9+4\sqrt{5}}\)

\(=\sqrt{\left(5-4\sqrt{5}+4\right)}+\sqrt{5+4\sqrt{5}+4}\)

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

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

\(=2\sqrt{5}\)

Answer 2

Answer 3

\(a.\sqrt{9-4\sqrt{5}}+\sqrt{9+4\sqrt{5}}=\left(4-\sqrt{5}\right)^2+\left(4+\sqrt{5}\right)=4-\sqrt{5}+4+\sqrt{5}=8\)

Answer 4

a) \(\sqrt{9+4\sqrt{5}}+\sqrt{9-4\sqrt{5}}=\sqrt{\left(2+\sqrt{5}\right)^2}+\sqrt{\left(\sqrt{5-2}\right)^2}\)

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

b) \(\sqrt{11+4\sqrt{6}}-\sqrt{11-4\sqrt{6}}=\sqrt{\left(2\sqrt{2}+\sqrt{3}\right)^2}-\sqrt{\left(2\sqrt{2}-\sqrt{3}\right)^2}\)

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

c) Mk chịu! Xl bn!

Answer 5

\(A=-\left(2-\sqrt{3}\right)+\left(2+\sqrt{3}\right)=-2+\sqrt{3}+2+\sqrt{3}=\sqrt{6}\)