Question

proof that underroot 3 is irrational number

Answer 1

Heya here is ur answer..
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PROOF:
Root 3 is irrational as it's=1.73205080756..which is an irrational number.
HOPE it is helpful

Answer 2

Let us assume √3 is rational number

√3=p/q where p,q are integers and q≠o
If p,q have common factor other than 1,then √3=a/b where a,b are coprime
Squaring on both sides
(√2)²=(a/b)²
2=a²/b²
a²/b²=2
a²/2=b²take this as equation 1
Here 2divides a² then2 also divide a
Let a =2c
Sub a=2c in equation 1
(2c)²/2=b²
4c²/2=b²
2c²=b²
c²=b²/2
b²/2=c²
Here 2 divides b² then 2 also divisable by b
From the above 2 is a factor of both a and b
But a and b are coprimes
Therefore this contribution has arrived due to our assumed is worng
So √2 is a irrational number
Hence proved