Răspuns:
1. Adevarat!
2. [tex]\sqrt{5}(2-\sqrt{3})[/tex]
Explicație pas cu pas:
1. [tex]m_{g}=\sqrt{a*b}[/tex]
[tex]m_{g}=\sqrt{5\sqrt{5}*25\sqrt{5}}[/tex]
[tex]m_{g}=\sqrt{125*5}[/tex]
[tex]m_{g}=\sqrt{5^{3}*5}[/tex]
[tex]m_{g}=\sqrt{5^{4}}=5^{2}=25[/tex]
[tex]25\in\mathbb{N}\implies m_{g}\in\mathbb{N}[/tex]
2. [tex]\sqrt{20}-\sqrt{15}=?[/tex]
[tex]20\:\big{|}2*5\\2\:\big{|}2\\1/\\\implies 20=2\sqrt{5}[/tex]
[tex]15\:\big{|}3\\5\:\big{|}5\\1/\\\implies 15 = 15[/tex]
[tex]2\sqrt{5}-\sqrt{15}=\sqrt{5}(2-\sqrt{3})[/tex]
