Question

prove that under root 6 is an irrational number​

Answer 1

Answer:

OK Here you go!!!

Step-by-step explanation:

MATHS

Prove that

6

is an irrational number

ANSWER

The following proof is a proof by contradiction.

Let us assume that

6

is rational number.

Then it can be represented as fraction of two integers.

Let the lowest terms representation be:

6

=

b

a

where b



=0

Note that this representation is in lowest terms and hence, a and b have no common factors

a

2

=6b

2

From above a

2

is even. If a

2

is even, then a should also be even.

⟹a=2c

4c

2

=6b

2

2c

2

=3b

2

From above 3b

2

is even. If 3b

2

is even, then b

2

should also be even and again b is even.

But a and b were in lowest form and both cannot be even. Hence, assumption was wrong and hence,

6

is an irrational number.