√7 is irrational prove it
Posted by Ganesh Kumar Sethy 10 months, 1 week ago
- 1 answers
Let us assume that 7 is rational. Then, there exist co-prime positive integers a and b such that 7=ba ⟹a=b7 Squaring on both sides, we get a2=7b2 Therefore, a2 is divisible by 7 and hence, ais also divisible by7 so, we can write a=7p, for some integer p. Substituting for a, we get 49p2=7b2⟹b2=7p2. This means, b2 is also divisible by 7 and so, b is also divisible by 7. Therefore, a and b have at least one common factor, i.e., 7. But, this contradicts the fact that a and bare co-prime. Thus, our supposition is wrong. Hence, 7 is irrational.
If (-5,3) and (5,3) are the two vertices of an equilateral triangle, then find co ordinate of the third vertex, given that origin lies inside the triangle. (Take root 3=1.7)
Posted by Devesh Singh 1 day, 6 hours ago
- 0 answers