Question

show that 4√2 Irnational number​

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.

Hope its help..

Answer 2

〰Given that :- 4√2

〰To prove :- 4√2 is an irrational number .

⚫We shall prove this by the method of Contraction . so let us assume that 4√2 is a Rational Number .

4√2 = r

√2 = r/4

Now, we know √2 is an irrational number.

So RHS { r/4 } cannot be rational . As then the equation will be false .

So our Assumption is Wrong .

Hence , 4√2 is an irrational number