Prove that 2 - root 3 is irrational
Answers
Answered by
69
Let 2-√3 be rational
2-√3=p/q
√3=p/q+2
√3=(p+2q)/q(Integer/Integer)
√3 is a irrational number
it shows our supposition was wrong
hence 2-√3 is a irrational number
hope it helps u
2-√3=p/q
√3=p/q+2
√3=(p+2q)/q(Integer/Integer)
√3 is a irrational number
it shows our supposition was wrong
hence 2-√3 is a irrational number
hope it helps u
dulpreet:
yr kya galti ha
Answered by
33
Answer:
Here, the given number is,
2 - √3
Let us assume that 2 - √3 is a rational number,
Then by the property of rational number,
Where, both p and q are integers, q ≠ 0,
Since, p and q are integers,
⇒ 2 - p and q are integers,
⇒ is a rational number such that q ≠ 0
But we know that √3 is an irrational number,
And, we can not equate a rational number and an irrational number,
Therefore, our assumption is wrong, 2 - √3 is not a rational number,
⇒ 2 - √3 is an irrational number.
Hence, Proved.
Similar questions