Question

[tex] \sqrt{3 + 2 \sqrt{2 } } - \sqrt{3 - 2 \sqrt{2} } [/tex]
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Answer 1

Verified answer

[tex]\sqrt{3+2\sqrt2}-\sqrt{3-2\sqrt2}=\sqrt{1+2\sqrt2+2}-\sqrt{1-2\sqrt2+2}=\\=\sqrt{(1+\sqrt2)^2}-\sqrt{(1-\sqrt2)^2}=|1+\sqrt2|-|1-\sqrt2|=\\=1+\sqrt2-(-1+\sqrt2)=1+\sqrt2+1-\sqrt2=2[/tex]