Question

prove that root 5 + root 2 is an irrational number

Answer 1

hii

proof: let us consider √5+√2 is rational number

therefore, √5+√2= p/q where, p and q are integers, and p and q are co- prime

(√5+√2)² = (p/q)²

5+2= p²/q²

7 = p²/q² ______________(1)

p²= 7q²

=> p is divisible by 7
=> p² is divisible by 7 _____________(2)

by taking another variable p=7m,

from (1)

(7m)² =7q²

49m² =7q²

7m² = q²

q² = 7m²

=> q is divisible by 7
=> q² is divisible by 7

That is our assumption is wrong
p and q both are divisible by 7
then √5+√2 is irrational.

hope it will help
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