Question

\(\sqrt{31-12\sqrt{3}}-\sqrt{31+12\sqrt{3}}\)

tính

Answer 1

\(\sqrt{31-12\sqrt{3}}-\sqrt{31+12\sqrt{3}}\)

\(=\sqrt{\left(3\sqrt{3}\right)^2-2.3\sqrt{3}.2+2^2}-\sqrt{\left(3\sqrt{3}\right)^2+2.3\sqrt{3}.2+2^2}\)

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

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

Answer 2

\(\sqrt{31-12\sqrt{3}}-\sqrt{31+12\sqrt{3}}\)

=\(\sqrt{27-12\sqrt{3}+4}-\sqrt{27+12\sqrt{3}+4}\)

=\(\sqrt{\left(3\sqrt{3}\right)^2-2.2.3\sqrt{3}+2^2}-\sqrt{\left(3\sqrt{3}\right)^2+2.2.3\sqrt{3}+2^2}\)

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

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

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

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

=-4

Answer 3

\(\sqrt{31-12\sqrt{3}}-\sqrt{31+12\sqrt{3}}\)

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

=-4