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27. Prove that 2- root 5 is irrational, given that root
5 is irrational. ​

By Iris

27. Prove that 2- root 5 is irrational, given that root
5 is irrational. ​

About the author
Iris



2.7.5 Show how to store a complete set of shortest paths in Floyds algorithm, using a matrix PrevPt[v, w], being the

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4. If the midpoint of the line segment joining (3, 4) and (k, 7) be on the line 2x + 2y +1 = 0, then find the
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2 thoughts on “27. Prove that 2- root 5 is irrational, given that root <br />5 is irrational. ​”

  1. If possible, let us assume 2+
    5
    ​
    is a rational number.
    2+
    5
    ​
    =
    q
    p
    ​
    where p,q∈z,q

    =0
    2−
    q
    p
    ​
    =−
    5
    ​

    q
    2q−p
    ​
    =−
    5
    ​

    ⇒−
    5
    ​
    is a rational number
    ∵
    q
    2q−p
    ​
    is a rational number
    But −
    5
    ​
    is not a rational number.
    ∴ Our supposition 2+
    5
    ​
    is a rational number is wrong.
    ⇒2+
    5
    ​
    is an irrational number.

    Reply

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