prove that
[tex] \sqrt{3 – \sqrt{5} } [/tex]
is an irrational number
​

1 thought on “<br />prove that<br />[tex] \sqrt{3 – \sqrt{5} } [/tex]<br />is an irrational number<br />​”

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

   [tex]:\implies[/tex] [tex]\sf{q(25p)=5-3+(q2p2)}[/tex]

   ⇒q(25p)=q22q2−p2

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