Question

Answer 1

\(a,\left(\sqrt{2}\right)^2=4< 25=5^2\Rightarrow\sqrt{2}< 5\Rightarrow-\sqrt{2}>-5\\ b,9=3+6;\left(2\sqrt{2}\right)^2=8< 9=3^2\\ \Rightarrow2\sqrt{2}< 3\Rightarrow6+2\sqrt{2}< 9\\ c,\left(\sqrt{2}+\sqrt{3}\right)^2=5+2\sqrt{6};3^2=9=4+5\\ \left(2\sqrt{6}\right)^2=24>16=4^2\\ \Rightarrow2\sqrt{6}>4\Rightarrow\sqrt{2}+\sqrt{3}>3\\ d,\left(\sqrt{11}-\sqrt{3}\right)^2=14-2\sqrt{33};2^2=4=14-10\\ \left(2\sqrt{33}\right)^2=132>100=10^2\\ \Rightarrow-2\sqrt{33}< 10\\ \Rightarrow\sqrt{11}-\sqrt{3}< 10\)