Question

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

Answer 1

\(\sqrt{7-4\sqrt{3}}+\sqrt{13-4\sqrt{3}}=\sqrt{\left(\sqrt{3}-1\right)^2}+\sqrt{\left(2\sqrt{3}-1\right)^2}=\left|\sqrt{3}-1\right|+\left|2\sqrt{3}-1\right|\)

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

Answer 2

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

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

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

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

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