Question

Show that root 3+root 2 is irrational

Answer 1

HEY THERE.....
UR ANSWER.....
ROOT 3+ ROOT 2 = 5
THEREFORE, FIVE IS AN IRRATIONAL NUMBER....
THANKS FOR ATTEND ME.....
PLZZZ MARK AS BRAINLIEST....

Answer 2

consider ,3+✓2 is a rational no
=> 3✓2 =p/q (equation 1)
p and q are integers and Co prime nos ( statement one )
q is not = 0
on equation 1
squaring on LHS and RHS
(3✓2)^2 = (p/q)^2
9*2= p^2/q^2
18q^2 = p^2. (equation 3)
=> 18 divides p^2
=> 18 divides p
=> p is a factor of 18. (equation 2)(statement a)
from eq 2
p = 18m
square on LHS and RHS
p^2 = 18m^2. (equation 4)
(eq 3 in eq 4)

p^2 = 18m^2 = 18q^2
18m^2= q^2

=> 18 divides q^2
18 divides q
18 is a factor of q. (statement b)
statement a and b => 18 is a common factor of p &q.
but statement one says hcf = 1 only
which is contradiction
therefore 3+✓2 is a irrational no