Question

Prove that 6+2+root5 is irrational

Answer 1

Answer:

let us assume that 6 -2 root5 is a rational number.

Therefore ,

6 -2root 5 = p / q where p and q are integers and q ia not equal to 0.

6 - 2root 5 = a / b where a and b are co-prime .

Therefore ,

This contradicts the fact that root 5 is rational .

This is because of our weong assumption that 6 - 2root 5 is rational .

Therefore 6 - 2 root 5 is irrational

Step-by-step explanation:

Answer 2

Step-by-step explanation:

ANSWER

Assume that 3+2

5

is rational. Then,

3+2

5

=

b

a

5

=

2b

a−3b

This gives that

2b

a−3b

is rational but

5

is an irrational number, therefore, the assumption is wrong.

Hence, 3+2

5

is irrational.