Question

Show that 6+root2 is irrational

Answer 1

Answer:

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

Since , a and b are integers , is rational ,and so √2 is rational.

But this contradicts the fact that √2 is irrational.

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

•••♪

plz mark this as brainlist answer

Answer 2

$\huge \purple{ \mathtt{ \fbox{ \: Solution : \: \: }}}$

Let us assume , to the contrary , that 6 + √2 is rational

Thus

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

Since a and b are integers , we get $\sf \frac{a - 6b}{b}$ is rational and so √2 is rational

But this contradicts the fact that √2 is irrational

So , we conclude that 6 + √2 is irrational

_________________________

#answerwithquality #BAL