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

In this chapter, we provide KSEEB SSLC Class 9 Maths Chapter 1 Number Systems Ex 1.2 for English medium students, Which will very helpful for every student in their exams. Students can download the latest KSEEB SSLC Class 9 Maths Chapter 1 Number Systems Ex 1.2 pdf, free KSEEB SSLC Class 9 Maths Chapter 1 Number Systems Ex 1.2 pdf download. Now you will get step by step solution to each question.

## Karnataka Board 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.
True. Because 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.
False. Value of m−−√ is not netagive number.

(iii) Every real number is an irrational number.
False. Because set of real numbers contain both rational and irrational numbers. But 2 is a rational number but not 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.
Square root of all positive integers is not an irrational number.
E.g. 4–√ = 2 Rational number.
9–√ = 3 Rational number.

Question 3.
Show how 5–√ can be represented on the number line.
5–√ can be represented on number line: In the Right angled ∆OAB ∠OAB = 90°.
OA = 1 cm, AB = 2 cm., then
As per Pythagoras theorem,
OB2 =OA2 + AB2
= (1)2 + (2)2
= 1 + 4
OB2 = 5
∴ OB = 5–√
If we draw semicircles with radius OB with ‘O’ as centre, value of 5–√ on number line
5–√ = OM = +2.3
and 5–√ = ON = -2.3 (accurately).

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 P1P22 perpendicular to OP1 of unit length (see fig.). 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 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–√,……
Classroom activity : i) OA = 1 Unit, AB = 1 Unit, ∠A = 90°,
∴OB2 = OA2 + AB2
= (1)2 + (1)2
= 1 + 1
OB2 = 2
∴OB = 2–√
Similarly, square root spiral can be continued.

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