CBSE Class 9th Mathematics Solution
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Solutions for NCERT Class 9 Mathematics Chapter 1 – NUMBER SYSTEMS – Exercise 1.2

Exercise 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,  All numbers are real number and they can be shown on number line

(ii) False, Every points on the number line are real number , they can be whole number , they can be fraction number

this is not necessary that they are natural number

(iii) False, Real number contains both rational number and irrational number

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, square roots of all positive integers is not irrational because there are rational number also

example :

4

= 2 and 2 is rational number can be written as 2/1.

 

Question 3. Show how√ 5 can be represented on the number line

Solution:

To draw √5 we applying Pythagoras theorem

hypotenuse² = base²+height²

=22+12

=√4+1

=√5

consider 5  as radius and draw arc to line that meets point p.

P is the point represent the  root 5.

Question 4. Classroom activity (Constructing the ‘square root spiral’) : 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 OP1 of unit length. Draw a line segment P1 P2 perpendicular to OP1
of unit length (see Fig. 1.9).

Now draw a line segment P2  P3 perpendicular to OP2 . Then draw a line segment P3 P4 perpendicular to OP3. Continuing in
this manner, you can get the line segment Pn–1Pn
by
drawing a line segment of unit length perpendicular to OPn–1.

In this manner, you will
have created the points P2, P3,…., Pn,… ., and joined them to create a beautiful spiral depicting 2, 3, 4, …

Solution:

following steps to draw

  1. Mark a center point O.
  2. From the point O, draw a horizontal line OA of length 1 cm.
  3. From the point A, draw a perpendicular AB of length 1 cm to the OA.
  4. Now, join OB, where OB =  √2.  ∵ Pythagoras theorem 
  5. then, from point B, draw a line perpendicular to OB  of length 1 cm. Mark the end point as C.
  6. Join OC, where OC = √3
  7. Repeat steps 4, 5, 6 for  √4, √5,  √6, …
  8. this is  your square root spiral .

 

You can find the solutions for Class 6 Mathematics previous exercises from here

  1. Excercise1.3

Tags: 9th class maths solution, 9th class ncert chapter 1 solution, 9th class maths solution chapter 1

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