Prove that
[tex] \sqrt{5} [/tex]
is an irrational number​

Prove that
[tex] \sqrt{5} [/tex]
is an irrational number​

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

  1. [tex]\huge{\boxed{\mathfrak\blue{\boxed{\mathfrak\blue{\boxed{\mathfrak\blue{\boxed{\mathfrak\blue{\boxed{\mathfrak\blue{\boxed{\mathfrak\blue{\boxed{\mathfrak\blue{\boxed{\mathfrak\blue{\fcolorbox{red}{black}{\red{Answer}}}}}}}}}}}}}}}}}}}[/tex]

    Let us assume√5 is rational.

    √5=[tex]\frac{p}{q}[/tex] [p and q are co-prime]

    p=√5q …(1)

    p²=5q [Squaring both the sides]

    [tex]\frac{p²}{5}=q²[/tex]…(2)

    p² divides 5, p also divides 5.

    p=5m [m is any integer]

    From equation 1,

    √5q=5m

    q=[tex]\frac{5m}{√5}[/tex]

    q=√5m

    q²=5m² [Squaring both the sides]

    5 divides both p and q.

    But p and q are co-primes.

    It means our assumption is wrong.

    √5 is irrational

    _______________________________________

Leave a Comment