Factorise

Algebra Level 3

Simplify

3 + 2 2 . \sqrt{ 3 + 2 \sqrt{2} }.

Cannot be Factorised 3 + 1 \sqrt{3+1} 2 + 1 \sqrt{2}+1 None of The Above 3 + 1 \sqrt{3}+1

Aditya Trivedi by Aditya Trivedi , 19, India

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2 solutions

Aditya Trivedi
Jan 13, 2015

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

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

( 2 ) 2 + ( 1 ) 2 + ( 2 ) ( 2 ) ( 1 ) \sqrt{(\sqrt2)^2+(1)^2+(2)(\sqrt{2})(1)}

( ( 2 ) + ( 1 ) ) 2 \sqrt{((\sqrt2)+(1))^2}

( 2 + 1 ) (\sqrt{2}+1)

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There is a statement : a + b = ( a + b ) + 2 a . b \sqrt{a} + \sqrt{b} = \sqrt{(a+b) + 2\sqrt{a.b}}

3 + 2 2 = ( 2 + 1 ) + 2 2.1 \sqrt{3 + 2\sqrt{2}} = \sqrt{(2+1) + 2\sqrt{2.1}}

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

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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