Question

prove that each of the following number is irritational 3-√2​

Answer 1

Answer:

+

2

Let

3

+

2

be a rational number.

⇒

3

+

2

=x

Squaring on both the sides, we get (

3

+

2

)

2

=x

2

⇒3+2+2×

3

×

2

=x

2

⇒x

2

−5=2

6

⇒

6

=

2

x

2

−5

Here, x is a rational number.

⇒x

2

is a rational number.

⇒x

2

−5 is a rational number.

⇒

2

x

2

−5

is also a rational number.

⇒

2

x

2

−5

=

6

is a rational number.

But

6

is an irrational number.

⇒

2

x

2

−5

is an irrational number.

⇒x

2

−5 is an irrational number.

⇒x

2

is an irrational number.

⇒x is an irrational number.

But we have assume that x is a rational number.∴ we arrive at a contradiction. So, our assumption that

3

+

2

is a rational number is wrong.

∴

3

+

2

is an irrational number.