Question
Simplify: $\sqrt{3-2\sqrt2}.$
✓
Answer
We are asked to simplify $\sqrt{3-2\sqrt2}.$ It can be written in the form $(\text{a}-\text{b})^2=\text{a}^2+\text{b}^2-2\text{ab}$ as$\sqrt{3-2\sqrt2}=\sqrt{2+1-2\times1\times\sqrt2}$
$=\sqrt{\big(\sqrt2\big)^2+(1)^2-2\times1\times\sqrt2}$
$=\sqrt{\big(\sqrt2-1\big)^2}$
$=\sqrt2-1$
Hence the value of given expression is $\sqrt2-1.$
$=\sqrt{\big(\sqrt2\big)^2+(1)^2-2\times1\times\sqrt2}$
$=\sqrt{\big(\sqrt2-1\big)^2}$
$=\sqrt2-1$
Hence the value of given expression is $\sqrt2-1.$
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