1.

(√2-2)², Classify the given number as rational or irrational.

Answer»

GIVEN number = ( √2 - 2 )²


This is of the form ( a - b )²


We know that ( a - b )² = a² - 2ab + b²


=> ( √2 - 2 )² = ( √2 )² - 2 ( √2 ) ( 2 ) + 2²


=> ( √2 - 2 )² = 2 - 4√2 + 4


=> ( √2 - 2 )² = 6 - 4√2


Since 6 - 4√2 is an irrational number ( As anything added with irrational number is an irrational number ), ( √2 - 2 )² is ALSO an irrational number.



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