Question

prove that 5 + root 2 is an irrational number ​

Answer 1

Step-by-step explanation:

let 5+root 2 is rational

Now 5 is rational and difference of two rational is always rational i.e.5+root2-5is rational

Root 2 is rational

Hence our proposal is wrong

It is irrational

Answer 2

Let us assume 5 + √2 is rational.

$so \: \: 5 + \sqrt{2} = \frac{a}{b}$

Here b is not equal to zero.

$\sqrt{2} = \frac{a}{b} - 5$

$\sqrt{2} = \frac{a - 5b}{b}$

For a and b are positive integers,

$\frac{a - 5b}{b} \: is \: rational$

So, that way √2 is rational.

But this contradicts the fact that √2 is irrational.

There fore 5-√2 is irrational

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