Question

Prove that 5- root 3 is irrational given that root 3 is irrational

Answer 1

Step-by-step explanation:

let us assume 5-√3 to be rational and is of the form p/q

5-√3= p

q

-√3= p -5

q

-√3 = p - 5q (taking LCM as q)

q

√3= 5q-p

q

LHS √3 is irrational and hence RHS 5q-p/q

is also irrational...and hence contradicts our assumption that 5-√3 is rational

hence 5-√3 is irrational

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Answer 2

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