KSEEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2

Students can Download Class 9 Maths Chapter 1 Number Systems Ex 1.2 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 9 Maths helps you to revise the complete Karnataka State Board Syllabus and to clear all their doubts, score well in final exams.

Karnataka State Syllabus 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.
Answer:
True. Because the set of real numbers contain both rational and irrational number.

(ii) Every point on the number line is of the form √m. where ‘m’ is a natural number.
Answer:
False. The value of √m is not a negative number.

(iii) Every real number is an irrational number.
Answer:
False. Because sets of real numbers contain both rational and irrational numbers. But 2 is a rational number but not an 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 rationed number.
Answer:
Square root of all positive integers is not irrational number.
E.g. \(\sqrt{\mathrm{4}}\) = 2 Rational number.
\(\sqrt{\mathrm{9}}\) = 3 Rational number.

Question 3.
Show how √5 can be represented on the number line.
Answer:
We know that √4 = 2
∴ \(\sqrt{5}=\sqrt{(2)^{2}+1^{2}}\)

Steps: Draw a straight line and mark the values as indicated.
Mark a point ‘A’ representing 2 on the number line.

Now construct AB of unit length perpendicular to OA. Then, taking O as center and OB as radius, draw an arc intersecting the number line at C.
C is representing √5.

Question 4.
Classroom activity.

Answer:
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 P₁P₂, perpendicular to OP₁ of unit length (see Fig 1.9). Now draw a line segment P₂P₃ perpendicular to OP₂. Then draw a line segment P₃P₄ perpendicular to OP₃. Continuing in this manner, you can get the line segment P_n-1P_n by 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 create a beautiful spiral depicting √2, √3, √4, ……