Question

giúp mình câu E,F,H

Answer 1

\(E=\sqrt{12-6\sqrt{3}}+\sqrt{21-12\sqrt{3}}\)

\(=\sqrt{9-2.3\sqrt{3}+3}+\sqrt{12-2.3.2\sqrt{3}+9}\)

\(=\sqrt{\left(9-3\right)^2}+\sqrt{\left(12-9\right)^2}\)

\(=\sqrt{6^2}+\sqrt{3^2}\)

\(=6+3=9\)

Answer 2

e) Ta có: \(E=\sqrt{12-6\sqrt{3}}+\sqrt{21-12\sqrt{3}}\)

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

\(=\sqrt{3}\)

f) Ta có: \(F=\sqrt{21-12\sqrt{3}}+\sqrt{21+12\sqrt{3}}\)

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

\(=4\sqrt{3}\)

h) Ta có: \(H=\sqrt{14+6\sqrt{5}}+\sqrt{14-6\sqrt{5}}\)

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

=6

Answer 3

\(F=\sqrt{21-12\sqrt{3}}+\sqrt{21+12\sqrt{3}}\)

\(=\sqrt{12-2.3.2\sqrt{3}+9}+\sqrt{12+2.3.2\sqrt{3}+9}\)

\(=\sqrt{\left(12-9\right)^2}+\sqrt{\left(12+9\right)^2}\)

\(=\sqrt{3^2}+\sqrt{21^2}\)

\(=3+21=24\)

Answer 4

\(H=\sqrt{14+6\sqrt{5}}+\sqrt{14-6\sqrt{5}}\)

\(=\sqrt{9+2.3\sqrt{5}+5}+\sqrt{9-2.3\sqrt{5}+5}\)

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

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

Answer 5

Bai E voi F minh nham, de minh lam lai

Answer 6

\(E=\sqrt{12-6\sqrt{3}}+\sqrt{21-12\sqrt{3}}\)

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

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

\(F=\sqrt{21-12\sqrt{3}}+\sqrt{21+12\sqrt{3}}\)

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

\(=2\sqrt{3}-3+2\sqrt{3}+3=4\sqrt{3}\)