Question

So sánh \(\sqrt{5}+\sqrt{7}\) và \(\sqrt{13}\)

Answer 1

√5 + √7 và √13

⇔√12 < √13.

Answer 2

Ta có : 2\(\sqrt{ }\)35>1

⇒2√35+ 12>13

⇔(5+7)\(^{ }\)^2>13

⇔5+7>√13

Answer 3

Ta có \(\left(\sqrt{5}+\sqrt{7}\right)^2=5+7+2\sqrt{5.7}=12+2\sqrt{35}=12+\sqrt{4.35}=12+\sqrt{140}\)Và \(\left(\sqrt{13}\right)^2=13=12+1\)

Vì \(\sqrt{140}>\sqrt{1}\Rightarrow\sqrt{140}>1\Rightarrow12+\sqrt{140}>12+1\Rightarrow\left(\sqrt{5}+\sqrt{7}\right)^2>\left(\sqrt{13}\right)^2\Rightarrow\sqrt{5}+\sqrt{7}>\sqrt{13}\)