Question

prove tht 3 - under root 2 is irrational​

Answer 1

Answer:

Let us assume, to the contrary, that 3

2

is

rational. Then, there exist co-prime positive integers a and b such that

3

2

=

b

a

⇒

2

=

3b

a

⇒

2

is rational ...[∵3,a and b are integers∴

3b

a

is a rational number]

This contradicts the fact that

2

is irrational.

So, our assumption is not correct.

Hence, 3

2

is an irrational number.

Answer 2

$\huge\mathrm{Hiiee!}$

Let $3 + \sqrt{2} = \frac{a}{b}$

$\sqrt{2} = \frac{a - 3b}{b}$

Since, $\frac{a}{b}$ is a rational number, $\frac{a - 3b}{b}$

is also a rational number.

But,$\sqrt{2}$

is an irrational number.

So,our supposition is wrong..

Hence,$3 + \sqrt{2}$ is an irrational number..