√(3+2√(2)) =√(2+1+2√(2)) =√((√(2))^2 + (1)^2 + 2 ×√(2)× 1) {Converting into (a+b)^2=a^2 + b^2 + 2ab} = √((√(2)+1)^2) = √(2) + 1 ...

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Rationalisation

Simplify : √3...

Question

Simplify : $\sqrt{3 + 2 \sqrt{2}}$ .

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Solution

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

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

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

${C o n v e r t i n g i n t o (a + b)^{2} = a^{2} + b^{2} + 2 a b}$

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

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