Question

prove 4+root2 irrational​

Answer 1

Answer:

here is your answer

Step-by-step explanation:

To prove :- 4√2 is an irrational number . ... Now, we know √2 is an irrational number. So RHS { r/4 } cannot be rational . As then the equation will be false .

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Answer 2

Answer:

Let’s assume on the contrary that 4 + √2 is a rational number.

Then, there exist co prime positive integers a and b such that

4 + √2 = abab

⇒ √2 = abab + 4

⇒ √2 = (a+4b)b(a+4b)b

⇒ √2 is rational

[∵ a and b are integers ∴ (a+4b)b(a+4b)b is a rational number]

This contradicts the fact that √2 is irrational. So, our assumption is incorrect.

Hence, 4 + √2 is an irrational number.