Question

Prove that 7 underoot2 is an irrational number, given that underoot2 is an irrational number.

Answer 1

Step-by-step explanation:

when one rational and one irrational numbers are added, they always result in an irrational sum

Answer 2

Answer:

Let us assume that 7+

2

is a rational number

Then. there exist coprime integers p, q,q



=0 such that

7+

2

=

q

p

=>

2

=

q

p

−7

Here,

q

p

−7 is a rational number, but 2

is a irrational number.

But, a irrational cannot be equal to a rational number.This is a contradiction.

Thus, our assumption is wrong.

Therefore

$7 + \sqrt{2}$ is a irrational number