Question

prove that the following are irrational 1/root2,7/root 5,6+root 2​

Answer 1

Answer:

Step-by-step explanation:

1/√2=√2/2rationalisation)

Assume that √2/2 is rational

Therefore,√2/2=a/b where a and b are co primes and b not equal to 0

√2/2=a/b

√2=2a/b

Since a and b are intergers,2a/b would be a rational number. But √2 is irrational.

This shows that the assumption of √2/2 as rational is wrong

Therefore, √2/2 or 1/√2 is irrational.

Same way,7/√5 Is irrational.

6+√2 , when assumed as rational, 6+√2=a/b

√2=a/b-6

But √2 is irrational

Therefore 6+√2 is irrational

Answer 2

Answer:

Hence 1/root2,7/root5, 6+ Root2 are irrational numbers