Question

Prove that √5 is irrational

Answer 1

Explanation:

Let us assume that √5 is rational.

∴ √5 = p/q     such that q ≠ 0 and    p  and q are co-primes i.e. HCF(p,q)=1

$=>5=\frac{p^2}{q^2}\\=>5q^2=p^2$

∴ 5 is a factor of $p^2$ which inturn means 5 is a factor of p

so, p can be 5m for some rational number m

∴$5q^2=(5m)^2\\=>q^2=5m^2$

which means 5 is a factor of q^2 as well as q.

but this contradicts our assumption that p and q are co-primes...

Hence, our assumption is wrong and √5 is irrational.

Answer 2

Step-by-step explanation:

hope it's help uuu....