1.

Show that 4√2 is an irrational number.​

Answer»

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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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