Question

demonstrati ca numerele radical 8 radical 76 radical 193 radical 555 radical 1000 sunt irationale folosind intercalarea numerelor scrise sub radicali intre doua patrate perfecte consecutive. ( Daca x,y e N
si n 2 < (x+1)2, atunci radical x este irational)​

Answer 1

Răspuns:

Explicație pas cu pas:

√8 ; √76 ; √193 ; √555 ; √1000  sunt irationale ?

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n² < x < (n+1)²  => √x irational

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2² < 8 < 3²  <=> 4 < 8 < 9  => √8 irational

8² < 76 < 9²  <=> 64 < 76 < 81 => √76 irational

13² < 193 < 14² <=> 169 < 193 < 196 => √193 irational

23² < 555 < 24² <=> 529 < 555 < 576 => √555 irational

31² < 1000 < 32² <=> 961 < 1000 < 1024 => √1000 irational

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