Question

Q.1 Show that 4√2 is an irrational number​

Answer 1

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Answer 2

Answer:

Assume that,

4

2

is a rational number.

Then, there exists coprime positive integers p & q such that

4

2

=

q

p

2

=

4q

p

(∵ p & q are integers)

⇒

4q

p

is rational

⇒

2

is rational

This contradict the fact that

2

is irrational. so our assumption is incorrect.

Hence 4

√2 is irritational.