Question

Prove that V2 is not
a rational number by
long divirsion Method
​

Answer 1

Step-by-step explanation:

Let us assume that

2

is a rational number

⇒

2

=

q

p

[

q

p

is in simplest form ]

⇒2q

2

=p

2

p

2

is even ⇒p is even ⇒p=2k

2q

2

=4k

2

⇒q

2

=2k

2

⇒q

2

is even

⇒q is even.

⇒p,q have 2 as a common factor which is contradiction to assumption.

∴

2

=

q

p

is a false

⇒

2

is not a rational.

Answer 2

Step-by-step explanation:

1

1 |2

| 1

| 1

As 1 is not the square number of any two digit number

root 2 is irrational

Hence proved