The correct option is B 1+√(2) √(3+ 2 √(2)) = √(1+2+2√(2)) =√((1)^2+(√(2))^2+2(1)(√(2))) =√((1+√(2))^2) =1+√(2) ...

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Operations on Binomial Surds

√3+2 √2=

Question

$\sqrt{3 + 2 \sqrt{2}}$ = __________________

$1 - \sqrt{2}$

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$1 + \sqrt{2}$

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

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$\sqrt{2}$

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Solution

The correct option is B
$1 + \sqrt{2}$

$\sqrt{3 + 2 \sqrt{2}}$ = $\sqrt{1 + 2 + 2 \sqrt{2}}$

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

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

= $1 + \sqrt{2}$

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