Question

√13 is irrational number

Answer 1

yes as it is non perfect square

Answer 2

Let _/13 be a rational number,

So, _/13=a/b where a and b are coprimes.

_/13b =a

Squaring on both sides,

13b^2=a^2------(1)

b^2=a^2/13

13 divides a^2,hence divides a

So, a=13c for some number c

Squaring on both sides,

a^2=169c^2

From eq.(1)

a^2=169c^2

13b^2=169c^2

b^2=13c^2

b^2/13=c^2

13 divides b^2,hence divides b

But this is contradictory to the fact that a and b are coprimes.

Hence, _/13 is an irrational number.

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