Question

prove that 1/3-√5 be a irrational number​

Answer 1

Answer:

Step-by-step explanation:

1/3 - √5

See in NCERT example, you will understand better from there.

Answer 2

Answer:

let 1/3 - root5 be rational

such that 1/3 -root5 = a/b where a and b are integers and b is not equal to 0

a/b +root5 = 1/3

root5 = 1/3-a/b

root 5= b/3b - 3a/3b

root 5= (b-3a)/3b

since 3, a and b are integers and operations on integers always gives rational number

therefore RHS is rational

but LHS is irrational

this contradiction has arisen due to our incorrect assumption

therefore, 1/3 -root5 is irrational

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