Question

prove that 6+root2
is irrational​

Answer 1

We will use contradictory method here. These type of questions are dealt with this method only.

Answer-

Let $6+\sqrt{2}$ be rational

Therefore, it can be written in the form of $\frac{a}{b}$ where b≠0 and HCF of a and b is 1 (i.e. they are coprimes)

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

$\sqrt{2} =\frac{a}{b} -6$

$\sqrt{2} =\frac{a-6b}{b}$

Here, $\frac{a-6b}{b}$ is rational.

Therefore, $\sqrt{2}$ is rational.

But, this contradicts the fact that $\sqrt{2}$ is irrational.

Hence, our assumption was wrong and $6+\sqrt{2}$ is irrational.

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Answer 2

Answer:

Answer is in the above picture

Hope it helps you