NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2.

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 9 |

Subject |
Maths |

Chapter |
Chapter 1 |

Chapter Name |
Number Systems |

Exercise |
Ex 1.2 |

Number of Questions Solved |
4 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2

**Question 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.**

**Solution:**

(i) True (∵ Real numbers = Rational numbers + Irrational numbers.)

(ii) False (∵ no negative number can be the square root of any natural number.)

(iii) False (∵ rational numbers are also present in the set of real numbers.)

**Question 2.**

**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:**

No, the square roots of all positive integers are not irrational.

e.g., √l6 = 4

Here, ‘4’ is a rational number.

**Question 3.**

**Show how √5 can be represented on the number line.**

**Solution:**

Now, take O as centre OP = √5 as radius, draw an arc, which intersects the line at point R. .

Hence, the point R represents √5.

**Question 4.**

**Classroom activity (constructing the ‘square root spiral’).**

**Solution:**

Take a large sheet of paper and construct the ‘square root spiral’ in the following fashion. Start with a point O and draw a line segment OP_{1}, of unit lengths Draw a line segment P_{1}, P_{2} perpendicular to OP_{1} of unit length (see figure).

Now, draw a line segment P_{2}P_{3} perpendicular to OP_{2}. Then draw a line segment P_{3}P_{4} perpendicular to OP_{3}. Continuing in this manner, you can get the line segment P_{n-1} P_{n} by drawing a line segment of unit length perpendicular to

OP_{n-1}. In this manner, you will have created the points P_{2}, P_{3},…… P_{n},….. and

joined them to create a beautiful spiral depicting √2,√3,√4,……

We hope the NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2, help you. If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2, drop a comment below and we will get back to you at the earliest.