Question

\(\sqrt{107+42\sqrt{2}}-3\)

Answer 1

\(\sqrt{107+42\sqrt{2}}-3=\sqrt{98+2\sqrt{882}+9}-3\)

= \(\sqrt{\left(\sqrt{98}+\sqrt{9}\right)^2}-3=\sqrt{\left(7\sqrt{2}+3\right)^2}-3\)

= \(\left|7\sqrt{2}+3\right|-3=7\sqrt{2}+3-3=7\sqrt{2}\)

Answer 2

\(\sqrt{107+42\sqrt{2}}-3=\sqrt{98+2.7\sqrt{2}.3+9}-3=\sqrt{\left(7\sqrt{2}+3\right)^2}-3=7\sqrt{2}+3-3=7\sqrt{2}\)