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.

- Number Systems Class 9 Ex 1.1
- Number Systems Class 9 Ex 1.2
- Number Systems Class 9 Ex 1.3
- Number Systems Class 9 Ex 1.4
- Number Systems Class 9 Ex 1.5
- Number Systems Class 9 Ex 1.6

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.**

- Every irrational number is a real number.
- Every point on the number line is of the form , where m is a natural number.
- Every real number is an irrational number.

**Solution:**

**(1) True** (∵ Real numbers = Rational numbers + Irrational numbers.)

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

**(3) 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.,

Here, ‘4’ is a rational number.

**Question 3.**

Show how can be represented on the number line.

**Solution:**

We know that, =

Draw of right angled triangle OQP, such that

OQ = 2 units

PQ= 1 unit

and ∠OQP = 90°

Now, by using Pythagoras theorem, we have

OP^{2} = OQ^{2} +PQ^{2
} = 2^{2} +1^{2
}= op= =

Now, take O as center OP = 45 as radius, draw an arc, which intersects the line at point R.

Hence, the point R represents .

**Question 4.**

A 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 length. Draw a line segment P_{1}P_{2} perpendicular to OP, 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 0P_{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 ,………..

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