Question

\(\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}\)

Answer 1

\(\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}=\sqrt{5}+1+\sqrt{5}-1=2\sqrt{5}\)

Answer 2

=\(\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{\left(\sqrt{5}-1\right)^2}\)

=\(\sqrt{5}+1+\sqrt{5}-1\)=2\(\sqrt{5}\)

Answer 3

=\(\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{\left(\sqrt{5-1}\right)^2}\)

=\(\sqrt{5}+1+\sqrt{5}-1\)

=\(2\sqrt{5}\)

Answer 4

\(\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}\)

\(=\sqrt{5}+1+\sqrt{5}-1\)

\(=2\sqrt{5}\)

Answer 5

\(\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}\)

=  \(\sqrt{6+4,472135955}+\sqrt{6-4,472135955}\)

\(=\sqrt{10,472135955}+\sqrt{2,4,472135955}\)

\(=3,236067977+1,572302756\)

= 4,808370733 \(\approx\) 5