Question

помогите пожалуйста даю 100 баллов ​

Answer 1

$\sqrt{21-14\sqrt{2}}=\sqrt{14}-\sqrt {7}\ \ \ |()^2\\\\21-14\sqrt{2}=14-2\sqrt{14}\cdot \sqrt {7}+7\\\\21-14\sqrt{2}=21-2\sqrt{2\cdot 7}\cdot \sqrt {7}\\\\21-14\sqrt{2}=21-2\sqrt{2}\cdot \sqrt{7}\cdot \sqrt {7}\\\\21-14\sqrt{2}=21-2\sqrt{2}\cdot 7\\\\21-14\sqrt{2}=21-14\sqrt{2}$

$\sqrt{107+20\sqrt{7}}=\sqrt{7}+10\ \ \ |()^2\\\\107+20\sqrt{7}=7+2\sqrt{7}\cdot 10+100\\\\107+20\sqrt{7}=107+20\sqrt{7}$