Question

Prove that
$\sqrt{5}$
is irrational.​

Answer 1

let √5 is not irrational

then√5 is rational

so,√5=a/b(where as a and b are co primes)

squaring on the both sides

(√5)^2=(a/b)^2

5. = a^2/b^2

5b^2 = a^2

if 5 divides a^2

then5 divides a

let a=5c

substituting ...

5b^2= (5c)^2

5b^2=25c^2

b^2. = 25/5c^2. by cancellation

5c^2= b^2

5 divides b^2

5 divides b

now 5 divides both a and b . so , a and b are the factor of 5 but not √5 . but √5 is irrational.

this is the contradiction .our assumption is wrong . √5 is irrational .

hence proved

plz mark me as brainliest plz