Prove that the following are irrationals:1/√2 ??????????????????????
Prove that the following are irrationals:
1/√2 ??????????????????????
Pawan Prajapati , 4 Years ago
Grade 12
10 grade maths> Prove that the following are irrationals:...
1 AnswersHarshit Singh
Dear Student
Let us assume1/√2is rational.
Then we can find co-prime x and y (y ≠ 0) such that1/√2= x/y Rearranging, we get,
√2= y/x
Since, x and y are integers, thus,√2is a rational number, which contradicts the fact that√2is irrational. Hence, we can conclude that1/√2is irrational.
Thanks
Let us assume1/√2is rational.
Then we can find co-prime x and y (y ≠ 0) such that1/√2= x/y Rearranging, we get,
√2= y/x
Since, x and y are integers, thus,√2is a rational number, which contradicts the fact that√2is irrational. Hence, we can conclude that1/√2is irrational.
Thanks
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