NCERT Solutions For Class 9 Math Chapter 1 Exercise – 1.2

NCERT Solutions For Class 9 Math Chapter – 1 Exercise – 1.2

Q1. State whether the following statements are true or false. Justify your answers.

Every irrational number is real number.

Solution:-

True.

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

Solution:-

False

Every real number is a irrational number.

Solution:-

False

Q2. Are the square roots of all positive integer 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 re not irrational.

For example,

√4 = 2 is rational.

√9 = 3 rational.

Hence , the square roots of positive integers 4 and 9 are not irrational.

Q3. Show how √5 can be represented on the number line.

Solution:-

Steps 1: Let line AB be of 2 unit on a number line.

Steps 2: At B , draw a perpendicular line BC of length 1 unit.

Steps 3: Join CA

Steps 4: Now , ABC is a right triangle Applying Pythagoras theorem

AB² + BC² = CA²

2² + 1² = CA² = 5

CA = √5 Thus , CA is a line of length √5 units.

Step 5: Taking CA as a radius and A as a center draw an arc touching the number line. The point at which number line get intersected by arc is at √5 distance from 0 a because it is a radius of the circle whose center was A.

Thus √5 is represented on the number line as shown in the figure.

Ncert solution class 9 chapter 1-1

Q4. 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 OP of unit length Draw a line segment P1P2 perpendicular to OP of unit length. Now a draw a line segment P₂P₃ perpendicular perpendicular to OP₂. Then draw a line segment P₃P₄. perpendicular to OP₃. Continuing in Fig 1.9:

Constructing this manner you can get the line segment P_n-1 Pn by square root spiral drawing a line segment of unit length perpendicular to OP_N-1 In this manner , you will have created the points P₂ , P₃ ……,P_{n- , ……….}and joined them to a create a beautiful spiral depicting √2 , √3 , √4, …..