√(3+2√(2)) =√(1+2+2√(2)) =√(1^2+ ( √(2) )^2+2× 1×√(2)) =√( ( 1+√(2) )^2) #160; #160; #160; #160; #160; #160; #160; # ...

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Rationalisation

Simplify √3...

Question

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

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Solution

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

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

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

$= \sqrt{{(1 + \sqrt{2})}^{2}}$ [ Using $a^{2} + b^{2} + 2 a b = (a + b)^{2}$ ]

$= 1 + \sqrt{2}$

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