Question

prove that root 5 is an irrational number

Answer 1

Hello dear friend.
Ur answer is here .

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Let take √5 as rational number
if a and b are two co-prime Number and b is not equal to 0
we can write √5 = a/b
multiple by b both sides we, get b√5 = a

To remove root , squaring on both sides,
we get 5b² = a² .............. ( 1 )
Therefore , 5 divides a² and according to theorem of rational number, for any prime number p which is divides a² then it will divide a also.

That means 5 will divide a .
so we can write a = 5c

putting value of a in equation ( 1 ) .we get
5b² = (5c)²
5b² = 25c²
Divides by 25 , we get b2/5 = c²
similarly , we get that b will divide by 5 .
and we have already get that a is divide by 5 but a and b are co-prime Number.
si it's condicts.

Hence , √5 is not a rational number , it is irrational.
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$hope \: \: its \: \: helps \: \: u$

Answer 2

This is your ans just put 5