State whether the following statements is false ?

Options

A. `(sqrt2)/3` is a rational number.
B. There are infinitely many rational between any two integers.
C. Number of rational numbers between 15 and 18 is infinite.
D. Rational are numbers which can be written in the form `p/q` , ` q ne 0,` p and q both are integers.

Answer

A

Explanation

(i) False , here `sqrt (2)` is an irrational number and 3 is a rational number, we know that when we divide irrational number by non - zero rational number it will always give an irrational number .
(ii) False, because between two consecutive integers (like 1 and 2) there does not exist any other interger.
(iii) False, becouse there any two rational numbers there exist infinitely many numbers.
(iv) true, because there are infinitely many numbers which cannot be written in the form `p/q q ne 0.` p,q both are integers and these numbers are called irrational numbers.
(v) False, e.g., Let an irrational number be `sqrt2 and root4(2)`
(a) ` (sqrt(2))^(2)=2` which is a rational number.
` root4(2)^(2)=sqrt2` , which is not a rational number.
Hence, square of an irrational number is not always a rational number.
(vi) False, `sqrt12/sqrt3=sqrt(4xx3)/sqrt3=(sqrt4xxsqrt3)/sqrt3=2xx1 = 2` which is a rational number.
`sqrt15/sqrt3=sqrt(5xx3)/sqrt3=(sqrt5xxsqrt3)/sqrt5= sqrt5` which is an irrational number.