Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

Solution:

The square roots of all positive integers are not irrational numbers.

For example, √4 = ± 2 which indicates that either 2 or -2 can be the square root of 4.

We see that both 2 and -2 are rational numbers because they can be expressed as 2/1 and -2/1 respectively.

☛ Check: NCERT Solutions Class 9 Maths Chapter 1

Video Solution:

Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

NCERT Solutions Class 9 Maths Chapter 1 Exercise 1.2 Question 2

Summary:

No, the square roots of all positive integers are not irrational. As we can take an example, √4 = ± 2 where 2 and -2 are both rational numbers.

☛ Related Questions:

• State whether the following statements are true or false. Justify your Answers. i) Every irrational number is a real number. ii) Every point on the number line is of the form √m, where m is a natural number. iii) Every real number is an irrational number.
• Show how √5 can be represented on the number line.