an
Que 2
prove that
that 5+ ste is irrational
numbeo
is being given
given that I
a
is irra

1 thought on “an<br />Que 2<br />prove that<br />that 5+ ste is irrational<br />numbeo<br />is being given<br />given that I<br />a<br />is irra”

1. Answer:

   Let us assume that √5 is a rational number.

   So it can be expressed in the form p/q where p,q are co-prime integers and q≠0

   ⇒ √5 = p/q

   On squaring both the sides we get,

   ⇒5 = p²/q²

   ⇒5q² = p² —————–(i)

   p²/5 = q²

   So 5 divides p

   p is a multiple of 5

   ⇒ p = 5m

   ⇒ p² = 25m² ————-(ii)

   From equations (i) and (ii), we get,

   5q² = 25m²

   ⇒ q² = 5m²

   ⇒ q² is a multiple of 5

   ⇒ q is a multiple of 5

   Hence, p,q have a common factor 5. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number

   √5 is an irrational number.

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