Let `C` be any circle with centre `(0,sqrt(2))dot` Prove that at most two rational points can be there on `Cdot` (A rational point is a point both of whose coordinates are rational numbers)

Let C be any circle with centre ( 0, sqrt( 2)) . Prove that at most two rational points can be there on C. ( A rational point is a point both of whose coordinates are rational numbers . )

Let C be any circle with centre (0,sqrt(2)) . Prove that at most two rational points can be there on C. (A rational point is a point both of whose cordinates are rational numbers)

Prove that all the vertices of an equilateral triangle can not be integral points (an integral point is a point both of whose coordinates are integers).

Prove that all the vertices of an equilateral triangle can not be integral points (an integral point is a point both of whose coordinates are integers).

Prove that sqrt(2) is not a rational number.

Prove that sqrt(2) is not a rational number.

Prove that sqrt2 is not a rational number.

Let p,q be chosen one by one from the set {1, sqrt(2),sqrt(3), 2, e, pi} with replacement. Now a circle is drawn taking (p,q) as its centre. Then the probability that at the most two rational points exist on the circle is (rational points are those points whose both the coordinates are rational)

Let p,q be chosen one by one from the set {1, sqrt(2),sqrt(3), 2, e, pi} with replacement. Now a circle is drawn taking (p,q) as its centre. Then the probability that at the most two rational points exist on the circle is (rational points are those points whose both the coordinates are rational)