Question

Show that 4root 2 is an irrational number

Answer 1

Answer:

〰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....⚫_⚫

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Answer 2

Answer:

4(2)^1/2 = (4^2 × 2 )^1/2

=(16×2)^1/2

= 32^1/2

this doesn't give us a perfect sqaure root... hence it's an irrational number.

Hope everything is clear