Question

Rút gọn các biểu thức sau:

\(A =\sqrt(1-\sqrt3)^2- \sqrt(\sqrt3+2)^2\)

\(B = \sqrt(2-\sqrt3)^2 + \sqrt(4-2\sqrt3)\)

\(C= \sqrt(15-6\sqrt6) + \sqrt(33-12\sqrt6)\)

 

Answer 1

\(A=\sqrt{\left(1-\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{3}+2\right)^2}\)

\(=1-\sqrt{3}-\sqrt{3}-2\)

\(=-2\sqrt{3}-1\)

\(B=\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{\left(4-2\sqrt{3}\right)^2}\)

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

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

Answer 2

\(A=\sqrt{\left(1-\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{3}+2\right)^2}\)

\(A=\sqrt{3}-1-\sqrt{3}-2\)

\(A=-3\)

\(B=\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{\left(4-2\sqrt{3}\right)}\)

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

\(B=1\)

Answer 3

\(A=\sqrt{\left(1-\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{3}+2\right)^2}\)

\(=\sqrt{3}-1-\sqrt{3}-2\)

\(=-3\)

\(B=\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{\left(4-2\sqrt{3}\right)}\)

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

\(=1\)