Question

rút gọn: \(\sqrt{7+4\sqrt{3}}+\sqrt{13-4\sqrt{3}}\)

Answer 1

\(\sqrt{7+4\sqrt{3}}+\sqrt{13-4\sqrt{3}}\)

= \(\sqrt{2^2+2.2.\sqrt{3}+\left(\sqrt{3}\right)^2}+\sqrt{\left(2\sqrt{3}\right)^2-2.2\sqrt{3}.1+1^2}\)

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

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

Answer 2

\(\sqrt{7+4\sqrt{3}}+\sqrt{13-4\sqrt{3}}\)

\(=\sqrt{2^2+2.2\sqrt{3+\left(\sqrt{3}\right)^2}}+\sqrt{\left(2\sqrt{3}\right)^2+2.2\sqrt{3}+1^2}\)

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

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

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

Chúc bạn học tốt!!!