Question

You have seen that √2 is irrational number show that. 2 + √2 is not a rrational number

Answer 1

SoluTion:

We know that, √2 is an irrational number (Also given in the question).

We've to show that 2 + √2 is not a rational one.

2 + √2

→ √2 = - 2

Here, -2 is a rational number and √2 is an irrational number.

Rational number can't be equal to irrational number. Hence, we can say that 2 + √2 is not a rational number.

We also know that, sum of rational and irrational number is irrational, so we can say that 2 + √2 is not a rational number.

Answer 2

Answer:

Let 2 + √2 be a rational number say r.

Then 2+ √2 = r

√2 = r - 2

But.√2 is an irrational number.

Therefore, r - 2 is also an irrational number.

⇒ r is an irrational number.

Hence our assumption r is a rational number is wrong.

Hence, 2 + √2 is not a rational number.