## Access Solutions to RS Aggarwal Mathematics For Class 9 Chapter 1 Real Numbers Exercises 1A to 1F:

__RS Aggarwal Class 9 Mathematics Solutions Chapter 1 Real Numbers Exercise 1A__

Question 1.

Solution:

A number in the form of

are all rational numbers.

Question 2.

Solution:

The given rational number are represented on a number line on given below :

Question 3.

Solution:

We know that, if a and b are two rational numbers, then a rational number between a and b will be

Question 4.

Solution:

Here, n = 3, x =

Question 5.

Solution:

Here, n=5, x =

Question 6.

Solution:

Here, n = 6, x = 3, y = 4

Question 7.

Solution:

Here, n = 16, x = 2.1, y = 2.2

__RS Aggarwal Class 9 Mathematics Solutions Chapter 1 Real Numbers Exercise 1B__

Question 1.

Solution:

We know that a fraction

Hence.

(i)

Question 2.

Solution:

Question 3.

Solution:

(i) Let,x = 0.

Then, 10x = 3.3333….

Question 4.

Solution:

(i) True, because set of natural numbers is a subset of whole number.

(ii) False, because the number 0 does not belong to the set of natural numbers.

(iii) True, because a set of integers is a subset of a rational numbers.

(iv) False, because the set of rational numbers is not a subset of whole numbers.

(v) True, because rational number can be expressed as terminating or repeating decimals.

(vi) True, because every rational number can be express as repeating decimals.

(vii) True, because 0 =

__RS Aggarwal Class 9 Mathematics Solutions Chapter 1 Real Numbers Exercise 1C__

Question 1.

Solution:

Irrational numbers : Numbers which are not rational numbers, are called irrational numbers. Rational numbers can be expressed in terminating decimals or repeating decimals while irrational number can’t.

Question 2.

Solution:

(i) √4 = ±2, it is a rational number

(ii) √196 = ±14 it is a rational number

(iii) √21 It is irrational number.

(iv) √43 It is irrational number.

(v) 3 + √3 It is irrational number because sum of a rational and an irrational number is irrational

(vi) √7 – 2 It is irrational number because difference of a rational and irrational number is irrational

(vii)

(viii) 0.

(ix) 1.232332333…. It is irrational number because it not repeating decimal

(x) 3.040040004…. It is irrational number because it is not repeating decimal.

(xi) 3.2576 It is rational number because it is a terminating decimal.

(xii) 2.3565656…. = 2.3

(xiii) π It is an irrational number

(xiv)

Question 3.

Solution:

(i) Let X’OX be a horizontal line, taken as the x-axis and let O be the origin. Let O represent 0.

Taken OA = 1 unit and draw AB ⊥ OA such that AB = 1 unit. Join OB, Then,

Question 4.

Solution:

Firstly we represent √5 on the real line X’OX. Then we will find √6 and √7 on that real line.

Now, draw a horizontal line X’OX, taken as x-axis

Question 5.

Solution:

(i) 4 + √5 : It is irrational number because in it, 4 is a rational number and √5 is irrational and sum of a rational and an irrational is also an irrational.

(ii) (-3 + √6) It is irrational number because in it, -3 is a rational and √6 is irrational and sum or difference of a rational and irrational is an irrational.

(iii) 5√7 : It is irrational because 5 is rational and √7 is irrational and product of a rational and an irrational is an irrational.

(iv) -3√8 : It is irrational because -3 is a rational and √8 is an irrational and product of a rational and an irrational is also an irrational.

(v)

(vi)

Question 6.

Solution:

(i) True.

(ii) False, as the sum of two irrational number is irrational is not always true.

(iii) True.

(iv) False, as the product of two irrational numbers is irrational is not always true.

(v) True.

(vi) True.

(vii) False as a real number can be either rational or irrational.

__RS Aggarwal Class 9 Mathematics Solutions Chapter 1 Real Numbers Exercise 1D__

Question 1.

Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

(i) Draw a line segment AB = 3.2 units (cm) and extend it to C such that BC = 1 unit.

(ii) Find the mid-point O of AC.

(iii) With centre O and OA as radius draw a semicircle on AC

(iv) Draw BD ⊥ AC meeting the semicircle at D.

(v) Join BD which is √3.2 units.

(vi) With centre B and radius BD, draw an arc meeting AC when produced at E.

Then BE = BD = √3.2 units. Ans.

Question 6.

Solution:

(i) Draw a line segment AB = 7.28 units and produce is to C such that BC = 1 unit (cm)

(ii) Find the mid-point O of AC.

(iii) With centre O and radius OA, draw a semicircle on AC.

(iv) Draw a perpendicular BD at AC meeting the semicircle at D

Then BD = √7.28 units.

(v) With centre B and radius BD, draw an arc which meet AC produced at E.

Then BE = BD = √7.28 units.

Question 7.

Solution:

(A) For Addition

(i) Closure property: The sum of two real numbers is always a real number.

(ii) Associative Law : (a + b) + c = a + (b + c), for all values of a, b and c.

(iii) Commutative Law : a + b = b + a for all real values of a and b.

(iv) Existance of Additive Identity : 0 is the real number such that: 0 + a = a + 0 = afor every real value of a.

(v) Existance of addtive inverse : For each real value of a, there exists a real value (-a) such that a + (-a) = (-a) + a = 0, Then (a) and (-a) are called the additive inverse of each other.

(v) Existence of Multiplicative Inverse. For each non zero real number a, there exists a real number

a and

(B) Multiplication

(i) Closure property: The product of two real numbers is always a real number.

(ii) Associative law : ab(c) = a(bc) for all real values of a, b and c

(iii) Commutative law : ab=ba for all real numbers a and b

(iv) Existance of Multiplicative Identity: clearly it is a real number such that 1.a = a.1 = a for every value of a.

__RS Aggarwal Class 9 Mathematics Solutions Chapter 1 Real Numbers Exercise 1E__

Rationalise the denominator of each of the followings :

Question 1.

Solution:

Here,RF of √7 is √7

Question 2.

Solution:

Here RF √3 is √3

Question 3.

Solution:

Here RF of

Question 4.

Solution:

Here RF is √5 + 2

Question 5.

Solution:

Here RF is 5 – 3√2

Question 6.

Solution:

Here RF is √6 + √5

Question 7.

Solution:

Here RF = √7 – √3

Question 8.

Solution:

Here RF = √3 – 1

Question 9.

Solution:

Here RF = (3-2√2)

Find the values of a and b in each of the following :

Question 10.

Solution:

(Multiplying and dividing by √3+1)

Question 11.

Solution:

(Multiplying and dividing by 3+√2)

Question 12.

Solution:

In

(Multiplying and dividing by 5-√6)

Question 13.

Solution:

In

(Multiplying and dividing by 7-4√3)

Question 14.

Solution:

Question 15.

Solution:

Question 16.

Solution:

x = (4-√15)

Question 17.

Solution:

x = 2+√3

Question 18.

Solution:

__RS Aggarwal Class 9 Mathematics Solutions Chapter 1 Real Numbers Exercise 1F__

Question 1.

Solution:

We know that

ap x aq = ap+q

∴ Therefore

Question 2.

Solution:

We know that

ap ÷ aq = ap-q

Therefore

Question 3.

Solution:

We know that

ap x bp = (ab)p

Therefore

Question 4.

Solution:

We know that

(ap)q =apq

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

__Access More:__

Class: 6 | Class: 7 | Class: 8 | Class: 9 | Class: 10 |
---|---|---|---|---|

Maths | Maths | Maths | Maths | Maths |

Science | Science | Science | Science | Science |

Social Science | Social Science | Social Science | Social Science | Social Science |

English | English | English | English | English |

Hindi | Hindi | Hindi | Hindi | Hindi |

Extra Subjects | Extra Subjects | Extra Subjects | Extra Subjects | Extra Subjects |