Question

Comparati numerele: 6√2 si 4√5; -2√3 si -3√2; -3√7 si -2√15

Answer 1

[tex]\it a=6\sqrt2=\sqrt{6^2\cdot2}=\sqrt{36\cdot2}=\sqrt{72} \\\;\\ b=4\sqrt5=\sqrt{4^2\cdot5}=\sqrt{16\cdot5}=\sqrt{80} \\\;\\ \sqrt{72}\ \textless \ \sqrt{80} \Rightarrow a\ \textless \ b[/tex]

-------------------------

[tex]\it a=-2\sqrt3 \Rightarrow -a = 2\sqrt3 =\sqrt{2^2\cdot3} =\sqrt{4\cdot3} =\sqrt{12} \\\;\\ b=-3\sqrt2 \Rightarrow -b = 3\sqrt2 =\sqrt{3^2\cdot2} =\sqrt{9\cdot2} =\sqrt{18} \\\;\\ \sqrt{12} \ \textless \ \sqrt{18} \Rightarrow -a\ \textless \ -b \Rightarrow a\ \textgreater \ b[/tex]