Question

Prove
that root 3*Root 5
is
an Irrational no:​

Answer 1

Answer:

let us suppose 3+root 5 is rational.

=>3+root 5 is in the form of p/q where p and q are integers and q is not =0

=>root5=p/q-3

​=>root 5=p-3q/q

as p, q and 3 are integers p-3q/3 is a rational number.

=>root 5 is a rational number.

but we know that root 5 is an irrational number.

this is an contradiction.

this contradiction has arisen because of our wrong assumption that 3+root 5 is a rational number.

hence 3+ root 5 is an irrational number.

Step-by-step explanation:

Answer 2

Answer:

$Let \: us \:assume \:that \: 3\sqrt{5} \:is \\an \: rational \: number$

$3\sqrt{5} = \frac{p}{q}\\ ( p,q \: are \: integers \: and \: q≠0 )$

$\implies \sqrt{5} = \frac{p}{3q}$

$p,q \: are \: integers \: so, \: \frac{p}{3q}\:is \\rational , and \: \sqrt{5} \:is \: also \: rational.$

$But \: it \: contradicts \: that \: \sqrt{5} \: is \\irrarional .$

Therefore.,

$3\sqrt{5} \: is \: an \: irrational.$

•••♪