State, whether the following numbers is rational or not : ( 2 + 2… - Vidyadip

Question

State, whether the following numbers is rational or not : $( 2 + \sqrt2 )^2$

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Answer

$( 2 + \sqrt2 )^2 = 2^2 + 2 ( 2 ) ( \sqrt2 ) + ( \sqrt2 )^2$
$= 4 + 4\sqrt2 + 2$
$= 6 + 4\sqrt2$
Irrational number.

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