Is \sqrt{3-2\sqrt{2}}+1 = \sqrt{2} ? If so, why? How can it be proven?
D dmouthfan2028 New member Joined Feb 18, 2010 Messages 3 Apr 1, 2010 #1 Is \(\displaystyle \sqrt{3-2\sqrt{2}}+1 = \sqrt{2}\) ? If so, why? How can it be proven?
S soroban Elite Member Joined Jan 28, 2005 Messages 5,586 Apr 1, 2010 #2 Hello, dmouthfan2028! \(\displaystyle \text{Is }\sqrt{3-2\sqrt{2}}+1 \:=\: \sqrt{2}\text{ ?}\) \(\displaystyle \text{If so, why? }\:\text{ How can it be proven?}\) Click to expand... \(\displaystyle \text{We have: }\:x \;=\;\sqrt{3-2\sqrt{2}} + 1\) \(\displaystyle \text{Note that: }3- 2\sqrt{2} \;=\;(\sqrt{2}-1)^2\) \(\displaystyle \text{Hence: }\:\sqrt{3-2\sqrt{2}} + 1 \;=\;\sqrt{(\sqrt{2}-1)^2} + 1 \;=\;(\sqrt{2}-1) + 1 \;=\;\sqrt{2}\)
Hello, dmouthfan2028! \(\displaystyle \text{Is }\sqrt{3-2\sqrt{2}}+1 \:=\: \sqrt{2}\text{ ?}\) \(\displaystyle \text{If so, why? }\:\text{ How can it be proven?}\) Click to expand... \(\displaystyle \text{We have: }\:x \;=\;\sqrt{3-2\sqrt{2}} + 1\) \(\displaystyle \text{Note that: }3- 2\sqrt{2} \;=\;(\sqrt{2}-1)^2\) \(\displaystyle \text{Hence: }\:\sqrt{3-2\sqrt{2}} + 1 \;=\;\sqrt{(\sqrt{2}-1)^2} + 1 \;=\;(\sqrt{2}-1) + 1 \;=\;\sqrt{2}\)
