prove that (2+root 3 )is sn irrational number
Answers
Step-by-step explanation:
let 2+√3 is a rational number
.•.it can be written as 2+√3=p/q
where p and q are integers having no common factors.
2+√3=p/q
√3=p/q -2
√3=p-2q/q
we know that p-2q/q is a rational number and √3 is an irrational number.therefore √3 is not equal to p-2q/q.
Thus contradiction has arisen .
Hence, 2+√3 is an irrational number.
Answer:Let 2+root3 is a rational number
a/b=2+root 3. (on squaring both the sides)
a square / b square =4+3
a square=7b square
a square is divisible by 7
a is divisible by 7 (equation 1)
Let a = 7c square ( on squaring both the sides)
a square =14c square
7b square=14c square
b square = 7c square
b square is divisible by 7
b is divisible by 7(equation 2)
From equation 1 and 2 we get 7 is common factor of a and b. This contradicts that our assumption is wrong because a and b do not have any common factor other then 1 . So 2 + root 3 is an irrational number not a rational number.
Step-by-step explanation: