Question

सिद्ध कीजिए कि रूट 5 एक अपरिमेय संख्या है​

Answer 1

ANSWER

Let

5

be a rational number.

then it must be in form of

q

p

where, q



=0 ( p and q are co-prime)

5

=

q

p

5

×q=p

Suaring on both sides,

5q

2

=p

2

--------------(1)

p

2

is divisible by 5.

So, p is divisible by 5.

p=5c

Suaring on both sides,

p

2

=25c

2

--------------(2)

Put p

2

in eqn.(1)

5q

2

=25(c)

2

q

2

=5c

2

So, q is divisible by 5.

.

Thus p and q have a common factor of 5.

So, there is a contradiction as per our assumption.

We have assumed p and q are co-prime but here they a common factor of 5.

The above statement contradicts our assumption.

Therefore,

5

is an irrational number