Question

2+5 root 3 irrational.

Answer 1

Yes it is an irrational number

Answer 2

first we prove the
$\sqrt{3}$
irrational then the all term is proved as irrational




sol:

let us assumed to contrary , √3 is rational


$\sqrt{3 = \frac{a}{b} }$
where (a) and (b ) r Coprimes

√3b=a ------>(1)
squaring both sides
(√3b)^2 =a ^2
3b^2=a^2
b^2=a^2/3

from above
a is divisible by 3 ------>(2
a=3c ----->(3)




from (3) put in (1)



a=3c
√3b=3c similarly


b^2 is divisible by 3 ------->(4)







from. (2) and (4)
it is proved that (a) and (b) are not Coprimes therefore our supposition is wrong than √3 is irrational