Question

Answer 1

\(a,\left(\sqrt{25}\right)^2=25;\left(2\sqrt{6}\right)^2=24;25>24\Rightarrow\sqrt{25}>2\sqrt{6}\\ b,\left(\sqrt{17+15}\right)^2=17+15=32\\ \left(\sqrt{17}+\sqrt{15}\right)^2=32+2\sqrt{255}\\ 32< 32+2\sqrt{255}\left(2\sqrt{255}>0\right)\Rightarrow\sqrt{17+15}< \sqrt{17}+\sqrt{15}\\ c,\left(\sqrt{8}-\sqrt{5}\right)^2=13-4\sqrt{10}\\ \left(4\sqrt{10}\right)^2=160>144=12^2\Rightarrow4\sqrt{10}>12\\ \Rightarrow-4\sqrt{10}< 12\Rightarrow13-4\sqrt{10}< 13-12=1\\ \Rightarrow\sqrt{8}-\sqrt{5}< 1\)