Question

$how to prove that \sqrt{5} is irrattional.$

Answer 1

Explanation:

Let √5 be a rational number.

√5=a/b( where a and b are integers and bis not equal to 0.a and b are co-prime).

squaring on both the sides

5=a^2/b^2

5b^2=a^2......(1)

a^2 is divisible by 5

a is divisible by 5

a= 5c.......for some integer c.

squaring on both sides

a^2=25c^2........(2)

from (1) and(2)

5b^2=25c^2

b^2=5c^2

b^2 is divisible by 5

b is divisible by 5

Therefore a and b are not co-prime.

Therefore √5 is not a rational number.

It is irrational number.

Hence proved.

Hope it helps.

Answer 2

For better understanding go to YouTube