Question

√7 is irrational number​

Answer 1

Yes√7 is irrational number

Answer 2

Answer:

Yes √7 is irrational no.

Here is the prove

Lets assume ,to the contrary,that √7 is rational.

So, √7= a/b, (where a and b are the co-primes).

√7 = a/b

b√7 = a

(squaring both sides)

7b^2 = a^2 ( 7 divides a) -------1

So by thoram,(1.3), it follows that 7 divides a.

So, a = 7c ( for integer c)

(7c)^2 = 7b^2

49^2 = 7b^2

b^2 = 7c^2

Here , b^2 is divisible by 7

And that means that a and b are not co-primes

So, this incorrectness is arises due to our wrong asssumption that √7 is rational

HENCE, √7 is an irrational number.

(Note that ^2 here, reoresents square)

Thanks!!!!