Question

prove that
$\sqrt{3 - \sqrt{5} }$
is an irrational number
​

Answer 1

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 qp form where p,q are integers and q isn't equal to zero.

3+5=qp

3=qp−5

squaring on both sides,

3=q2p2-2.5(qp)+5

$:\implies$ $\sf{q(25p)=5-3+(q2p2)}$

⇒q(25p)=q22q2−p2