Question

Show that 4 √ 2 is an irracional​

Answer 1

Step-by-step explanation:

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.

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Answer 2

Show that 4

2

is an irrational number.

EASY

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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.