Question

Giúp mình với

II.nhân:\(\sqrt{A}\).\(\sqrt{B}\)=\(\sqrt{..............}\)(A≥0;B≥0)

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

b)\(\sqrt{13+30\sqrt{2}+\sqrt{9+4\sqrt{2}}}\)

c)\(\sqrt{6+2\sqrt{5}-\sqrt{13+\sqrt{48}}}\)

Answer 1

a) Ta có: \(\sqrt{2}\left(\sqrt{3-\sqrt{5}}-\sqrt{3+\sqrt{5}}\right)\)

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

\(=\sqrt{5}-1-\sqrt{5}-1=-2\)

b) Ta có: \(\sqrt{13+30\sqrt{2}+\sqrt{9+4\sqrt{2}}}\)

\(=\sqrt{13+30\sqrt{2}+2\sqrt{2}+1}\)

\(=\sqrt{14+32\sqrt{2}}\)

c) Ta có: \(\sqrt{6+2\sqrt{5}-\sqrt{13+\sqrt{48}}}\)

\(=\sqrt{6+2\sqrt{5}-2\sqrt{3}-1}\)

\(=\sqrt{5+2\sqrt{5}-2\sqrt{3}}\)