Ncert solutions Our top 5% students will be awarded a special scholarship to Lido.
Set your child up for success with Lido, book a class today!
1. 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. Looking to do well in your science exam ? Learn from an expert tutor. Book a free class!

(i) Every irrational number is a real number.

True

Irrational Numbers - A number is said to be irrational if it cannot be written in the p/q, where p and q are

integers and q ≠ 0.

i.e., Irrational numbers = 0, 19/30, 2, 9/-3, -12/7, √2, √5, , 0.102….

Real numbers - The collection of both rational and irrational numbers are known as real numbers.

i.e., Real numbers = √2, √5, , 0.102…

Therefore, Every irrational number is a real number, however, every real number is not irrational numbers.

(ii) Every point on the number line is of the form √m where m is a natural number.

False

The statement is false since as per the rule, a negative number cannot be expressed as square roots.

E.g., √9 =3 is a natural number.

But √2 = 1.414 is not a natural number.

Similarly, we know that there are negative numbers on the number line but when we take the root of a

negative number it becomes a complex number and not a natural number.

E.g., √-7 = 7i, where i = √-1

∴ The statement that every point on the number line is of the form √m, where m is a natural number is false.

(iii) Every real number is an irrational number.

False

The statement is false, the real numbers include both irrational and rational numbers. Therefore, every real

the number cannot be an irrational number.

Real numbers - The collection of both rational and irrational numbers are known as real numbers.

i.e., Real numbers = √2, √5, , 0.102…

Irrational Numbers - A number is said to be irrational if it cannot be written in the p/q, where p and q are

integers and q ≠ 0.

i.e., Irrational numbers = 0, 19/30, 2, 9/-3, -12/7, √2, √5, , 0.102….

∴ Every irrational number is a real number, however, every real number is not irrational.

Our top 5% students will be awarded a special scholarship to Lido. Lido

Courses

Teachers

Book a Demo with us

Syllabus

Science
English
Coding

Terms & Policies

NCERT Question Bank

Maths
Science

Selina Question Bank

Maths
Physics
Biology

Allied Question Bank

Chemistry