Question

prove that √3+√5 is an irrational number, given√3 is irrational!!​

Answer 1

Answer:

let root 3 + roof 5 be rational

root 3 + root 5 = P/q

(root 3 + root 5) sq=(P/q)sq

3 +5 + 2 root 15 = P sq/q Sq

root I5 = (Psq / qsq -7) 1/2

RHS is rational as all are integers

⇒ LHS is also rational but root 15 is irrational

⇒ root3 + root 5 is irrational

Step-by-step explanation:

$Hope \: it \: helps.$

Answer 2

Answer:

Answer

To prove :

√3 +√5 is irrational.

Let us assume it to be a rational number.

Rational numbers are the ones that can be expressed in p/q form where p,q are integers and q isn't equal to zero.

√3 + √5 = p/q

√3=p/q-√5

squaring on both sides,

3=p^2/q^2-2.√5(p/q) +5

⇒(2√5p)/q=5-3+(p^2) /(q^2)

⇒(2√5p)/q=2q^2-p^2/q^2

⇒ √5=2q^2-p^2/q^2.q/2p

⇒ √5=(2q^2-p^2) /2pq

As p and q are integers RHS is also rational.

As RHS is rational LHS is also rational i.e

5 is rational.

But this contradicts the fact that

5 is irrational.

This contradiction arose because of our false assumption.

so, √3 + √5 irrational.