Question

Cat face! Dau coroana! Multumesc!

Answer 1

.........................................................

Answer 2

FORMULA RADICALILOR COMPUSI:
$\boxed{\sqrt{a+-\sqrt{b}}=\sqrt{\frac{a+c}{2}}+-\sqrt{\frac{a-c}{2}};unde:c=\sqrt{a^{2}-b}}$

$\sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}=?$



$\sqrt{3+2\sqrt{2}}=\sqrt{3+\sqrt{8}}$

$c=\sqrt{3^{2}-8}=\sqrt{9-8}=\sqrt{1}=1$

$\sqrt{3+2\sqrt{2}}=\sqrt{\frac{3+1}{2}}+\sqrt{\frac{3-1}{2}}=\sqrt{\frac{4}{2}}+\sqrt{\frac{2}{2}}=\sqrt{2}+\sqrt{1}=\sqrt{2}+1$



$\sqrt{3-2\sqrt{2}}=\sqrt{3-\sqrt{8}}$

$c=\sqrt{3^{2}-8}=\sqrt{9-8}=\sqrt{1}=1$

$\sqrt{3-2\sqrt{2}}=\sqrt{\frac{3+1}{2}}-\sqrt{\frac{3-1}{2}}=\sqrt{\frac{4}{2}}-\sqrt{\frac{2}{2}}=\sqrt{2}-1=\sqrt{2}-1$



Deci:

$\sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}=(\sqrt{2}+1)-(\sqrt{2}-1)=\sqrt{2}+1-\sqrt{2}+1=2$