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Root 5 is a irrational number

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Root 5 is a irrational number

Posted by Annu Meena 6 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Sneha Singh 6 years, 10 months ago

Let root 5 be a rational number Then, √5= a/b Now by squaring both sides 5= a²/b² = 5b² = a²............(1) Here 5 divides a², Therefore 5 also divides a. Now let a= 5c where c is an integer Now by squaring both side, = A²= 25c² = 5b² = 25c². ( A²= 5b² from above) = B² = 5c² Here 5 divides b square Therefore 5 also divides b. Here a and b both have common factor 5 So our assumption was wrong Therefore root 5 is an irrational number

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CBSE > Class 10 > Mathematics