Question

Prove the following numbers are irrational. 6+√2

Answer 1

Step-by-step explanation:

please mark it as brilliant

Answer 2

Answer:

here the answer,

Step-by-step explanation:

6+√2 is irrational.

Step-by-step explanation:

Let us assume that 6+√2 is rational.

That is , we can find coprimes a and b (b≠0) such that

6+\sqrt{2}=\frac{a}{b}6+2=ba

\implies \sqrt{2}=\frac{a}{b}-6⟹2=ba−6

\implies \sqrt{2}=\frac{a-6b}{b}⟹2=ba−6b

Since , a and b are integers , \frac{a-6b}{b}ba−6b is rational ,and so √2 is rational.

But this contradicts the fact that √2 is irrational.

So, we conclude that 6+√2 is irrational.

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