Question

show that root5+root11 is irrational number​

Answer 1

Step-by-step explanation:

Let us consider root 5+root 11 is an rational number

So root 5 +root 11 =p/q (q# 0)

5+11 = p2/q2 (p, q are coprime)

5+11 p2 = q2

q2 is divisible by 5+11

q is also divisible by 5+11

q = 5+11 m ( m is any positive integer)

replacing q, we get

5+11p2 =5+11m

5+11p2 =25 +121m2

p2 = 5+11m2

p2 is divisible by 5 +11

p is also divisible by 5+11

p and q both are divisible by 5+11

Hence our assumptions was wrong

So root 5 and root 11 are irrational number