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Root 5 is a irrational number |
| Answer» Let root 5 be a rational numberThen, √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 integerNow by squaring both side, = A²= 25c² = 5b² = 25c². ( A²= 5b² from above) = B² = 5c²Here 5 divides b squareTherefore 5 also divides b.Here a and b both have common factor 5So our assumption was wrongTherefore root 5 is an irrational number | |