prove that √3 is irrational number
Answers
HEY! ANSWER IS:
√3 = 1.7320508...
As it is non repeated and non ending, it is irrational.
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Answer:
Proof =>if possible, let root 3 be rational and let its simple form a/b.
Then, a and b are integers having no common factors other than 1,and b not is equal to 0.
Now, root 3=a/b=>3=a^/b^[on squaring both sides]
=>3b^=a^..........(1)
=>3 divides a^ [3 divides 3b^]
Let a=3c for some integer C.
Putting a=3c in (1),we get
3b^=9c => b^=3C^
=>3 divides b^ [3 divides 3c^]
=>3 divides b
[3 is prime and 3 divides b^=>3divides]
Thus, 3 is a common factor of a and b.
But, this contradicts the fact that a and b have no common factors other than 1.
The contradiction arises by assuming that root 3 is rational.
Hence, root 3 is irrational.