State whether the following statements are true or false. Justify your answers. (i) Every irrational number is a real number.

(i) True Consider the irrational numbers and the real numbers separately.

We know that irrational numbers are the numbers that cannot be converted in the form p/q,where p and q are integers and q ≠ 0 .

We know that a real number is the collection of rational numbers and irrational numbers.

Therefore, we conclude that, yes every irrational number is a real number.

(ii) True Consider a number line. We know that on a number line, we can represent negative as well as positive numbers.

We know that we cannot get a negative number after taking square root of any number.

Therefore, we conclude that not every number point on the number line is of the form m, where m is a natural number .

(iii) False Consider the irrational numbers and the real numbers separately.

We know that irrational numbers are the numbers that cannot be converted in the p/q form √m, where p and q are integers and q ≠ 0.

We know that a real number is the collection of rational numbers and irrational numbers.

So, we can conclude that every irrational number is a real number. But every real

number is not an irrational number.

Therefore, we conclude that, every real number is not a rational number.