Question

19. Given that √2 is irrational, prove that (5+√2)2 is an irrational number.

Answer 1

given: √2 is Irrational

To proof: (5+√2)2 is an irrational number.

prove:

suppose that (5+√2)2 is an rational number

then we can write A/B = (5+√2)2

(•°• A and B are co-prime no. )

(•°• B is not equal to Zero)

here,

A/2B = (5+√2)

A/2B- 5 = √2

A-10B/2B = √2

L.H.S is rational

R.H.S is irrational

our supposition was wrong

hence (5+√2) 2 is irrational.

hope this answer help you