Question

show that 4 root 2 is an irrational number

Answer 1

let it be rational then we can write them in the form of p/q where p and q are integers...

then 4√2=p/q

√2 = p/4q

although p and q are integers then p/4q is rational and if √2 equal that it should also be rational but this contradict the fact that √2 is irrational...

hence our contradiction was wrong...hence 4√2 is proved to be irrational...

hope this helps you.... mark as brainliest

Answer 2

Answer:

Assume that,

42 is a rational number. 

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

42=qp

2=4qp (∵ p & q are integers)

⇒4qp is rational

⇒2 is rational

This contradict the fact that 2

is irrational. so our assumption is incorrect.

Hence 42 is irritational.

There is a sign of root before every 2