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√5is irrational |
| Answer» Let √5 be a rational number and a and b it\'s simplest form .√5=a/b on squaring both sides 5=a²/b² _____ 5b²=a²____ It shows that 5 divides a² then 5 divide a .Put the value of a =5c , Then 5b²=(5c)²_____ 5b²= 25c²_____ b²=5c²____ here 5divides b² then 5 divide b This contradict the fact that a and b are the simplest form of √5. As it is having 5as it\'s common factor. This happen because of our default assumption that √5 is a rational number. So , we conflude that √5 is an irrational number. | |