Question

prove that 5+root 2 is irrational.

Answer 1

Hey Friend
Here is your answer

To prove :- 5 + root 2 is irrational.
Proof :- Let root 2 is not irrational
So,root 2 is rational
root 2 = p/q ( q is not equal to 0)
root 2q = p
Squaring both sides
(root 2q) ^2 = (p)^2
2q^2 = p^2
So, p^2 is divisible by 2.
p is also divisible by 2
2m = p
2m = root 2q
Squaring both sides
(2m)^2 = (2q)^2
4m^2 = 2q^2
So, q^2 is divisible by 2
q is also divisible by 2.
While is wrong.
So, our supposition is wrong.
So, root 2 is irrational.
5 + root 2 is irrational ( 5 + Non - terminating + Non - repeating = Non - terminating + Non - repeating )

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