Question

Prove that 7root 5 by 3 is irrational

Answer 1

Let 7√5 /3 be a rational no. where 7√5/3=p/q p and q belong to integers

7√5/3=p/q

7√5=(p/q)3

√5=(p/q)3/7

here, LHS is an irrational no. and RHS is a rational no.

But, we know that irrational no. is not equal to a rational no.

=) This a contradiction due to our wrong assumption.

therefore, 7√5/3 is an irrational no.

If it is a 3 or 4 mark qs. then prove the irrationality of √5.