Prove that √5 is a is an irrational number. ​

Question

Prove that √5 is a
is an irrational number.

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Clara 2 days 2021-10-12T06:25:01+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-12T06:26:13+00:00

    Answer:

    2.236…….

    Step-by-step explanation:

    this is the ans because the no goes on so we can’t make it as rational number so it’s irrational number.

    0
    2021-10-12T06:26:13+00:00

    Let us assume that √5 is a rational number.

    Sp it t 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

    Hence proved

    hope it will help u….

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