NCERT Solutions Class 9th Maths Chapter – 1 Number System Exercise – 1.2

NCERT Solutions Class 9th Maths Chapter – 1 Number System

TextbookNCERT
Class9th
SubjectMathematics
Chapter1st
Chapter NameNumber system
GradeClass 9th Mathematics
Medium English
Sourcelast doubt

NCERT Solutions Class 9th Maths Chapter – 1 Number System Exercise – 1.2 In This Chapter We Will Learn About Euclid`s Division Lemma, The Fundamental Theorem of Arithmetic, Fundamental Theorem of Arithmetic, Revisiting irrational Numbers, with NCERT Solutions Class 9th Maths Chapter – 1 Exercise – 1.2.

NCERT Solutions Class 9th Maths Chapter – 1 Number System

Chapter – 1

Number Systems

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.

Solution – True
Because all rational numbers and all irrational numbers form the group (collection) of real numbers.

(ii) Every point on the number line is of the form √m, where m is a natural number.

Solution – False
Because negative numbers cannot be the square root of any natural number.

(iii) Every real number is an irrational number.

Solution –False
Because rational numbers are also a part 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. For example,
√4 = 2 is rational.
√9 = 3 is rational.
Question 3. Show how √5 can be represented on the number line.

Solution – Draw a number line and take point O and A on it such that OA = 1 unit.
Draw BA ⊥ OA as BA = 1 unit. Join OB = √2 units.
Now draw BB1 ⊥ OB such that BB1 = 1 unit. Join OB1 = √3 units.
Next, draw B1B2 ⊥ OB1 such that B1B2 = 1 unit.
Join OB2 = units.
Again draw B2B3 ⊥ OB2 such that B2B3 = 1 unit.
Join OB3 = √5 units.
ch 1 1.2
Take O as Centre and OB3 as radius, draw an arc which cuts the number line at D.
Point D represents √5 on the number line.
Question 4. 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 se  gment OP1, of unit lengths Draw a line segment P1, P2 perpendicular to OP1 of unit length (see figure). 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-1 Pn 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,……
NCERT Solutions Class 9th Maths Chapter - 1 Exercise - 1.2
Solution – Step 1: Mark a point O on the paper. Here, O will be the center of the square root spiral.
Step 2: From O, draw a straight line, OA, of 1cm horizontally.
Step 3: From A, draw a perpendicular line, AB, of 1 cm.
Step 4: Join OB. Here, OB will be of √2
Step 5: Now, from B, draw a perpendicular line of 1 cm and mark the end point C.
Step 6: Join OC. Here, OC will be of √3
Step 7: Repeat the steps to draw √4, √5, √6….NCERT Solutions Class 9th Maths Chapter - 1 Exercise - 1.2

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