Question

Simplify √(3+2√2)
$\sqrt{3 + 2 \sqrt{2} }$
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Answer 1

Answer:

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

Answer 2

$= > \sqrt{( \sqrt{3} + 2 \sqrt{2} ) }$

$= > \sqrt{1 + 2 + 2 \sqrt{2} }$

$= > \sqrt{ {(1)}^{2} + {( \sqrt{2}) }^{2} + 2 \sqrt{2} }$

$= > \sqrt{ {(1)}^{2} + 2 \sqrt{2} + {( \sqrt{2} )}^{2} }$

$= > \sqrt{(1 + \sqrt{2} )^{2} }$

$= > 1 \: + \: \sqrt{2}$

$\sqrt{3+2√2}$ = 1 + √2 ☑️