Question
Let $x=\sqrt{3+2 \sqrt{2}}-\sqrt{3-2 \sqrt{2}}$ and calculatc $x^{2}$. Is $x$ irrational?
Step 1
First, we can simplify the expression inside the square roots: $3+2\sqrt{2} = (\sqrt{2}+1)^2$ and $3-2\sqrt{2} = (\sqrt{2}-1)^2$ Now we can rewrite $x$ as: $x = \sqrt{(\sqrt{2}+1)^2} - \sqrt{(\sqrt{2}-1)^2}$ Since the square root of a number squared is the Show more…
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Key Concepts
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