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

Question

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

in progress 0
Eloise 3 months 2021-07-24T11:57:16+00:00 1 Answers 0 views 0

Answers ( )

    0
    2021-07-24T11:59:08+00:00

    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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