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