Question

prove that root 5 is an irrational no
plz tell me ​

Answer 1

$\huge{\mathcal{\purple{S}\green{O}\pink{L}\blue{U}\purple{TI}\green{O}\pink{N}}}:$

Let ,$√5$ be a rational number

then it must be in form of $\frac{p}{q}$where, q is not equal to 0.( p and q are co-prime)

$√5=p/q$

$√5×q=p$

Squaring on both sides....

$5q²= p²$..............(1)

$p²$ is divisible by 5.

So, p is also divisible by 5.

$p=5c$

Squaring on both sides....

$p²=25c².$.................. (2)

Put the value of p² in equation (1)

$5q²=25c²$

$q²=5c$

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.

Hope it helps you frnd.........✌