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Question-174755




Question Number 174755 by mnjuly1970 last updated on 10/Aug/22
Commented by kaivan.ahmadi last updated on 11/Aug/22
I⊆(√I),J⊆(√J)⇒I+J⊆(√I)+(√J)  ⇒(√(I+J))⊆(√((√I)+(√J)))  on the other hand  (√I)+(√J)⊆(√(I+J))⇒(√((√I)+(√J)))⊆  (√(√(I+J)))=(√(I+J))  ■
$${I}\subseteq\sqrt{{I}},{J}\subseteq\sqrt{{J}}\Rightarrow{I}+{J}\subseteq\sqrt{{I}}+\sqrt{{J}} \\ $$$$\Rightarrow\sqrt{{I}+{J}}\subseteq\sqrt{\sqrt{{I}}+\sqrt{{J}}} \\ $$$${on}\:{the}\:{other}\:{hand} \\ $$$$\sqrt{{I}}+\sqrt{{J}}\subseteq\sqrt{{I}+{J}}\Rightarrow\sqrt{\sqrt{{I}}+\sqrt{{J}}}\subseteq \\ $$$$\sqrt{\sqrt{{I}+{J}}}=\sqrt{{I}+{J}} \\ $$$$\blacksquare \\ $$$$ \\ $$$$ \\ $$

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