SSC (English Medium) Class 9Maharashtra State Board
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# Balbharati solutions for Class 9 Algebra chapter 2 - Real Numbers

## Chapter 2: Real Numbers

Practice Set 2.1Practice Set 2.2Practice Set 2.3Practice set 2.3Practice Set 2.4Practice Set 2.5Problem Set 2Problem set 2Problem Set2

#### Chapter 2: Real Numbers Exercise Practice Set 2.1 solutions [Page 21]

Practice Set 2.1 | Q 1.1 | Page 21

Classify the decimal form of the given rational number into terminating and non-terminating recurring type.

13/5

Practice Set 2.1 | Q 1.2 | Page 21

Classify the decimal form of the given rational number into terminating and non-terminating recurring type.

2/11

Practice Set 2.1 | Q 1.3 | Page 21

Classify the decimal form of the given rational number into terminating and non-terminating recurring type.

29/16

Practice Set 2.1 | Q 1.4 | Page 21

Classify the decimal form of the given rational number into terminating and non-terminating recurring type.

17/125

Practice Set 2.1 | Q 1.5 | Page 21

Classify the decimal form of the given rational numbers into terminating and non-terminating recurring type.

11/6

Practice Set 2.1 | Q 2 | Page 21

Write the following rational numbers in decimal form.

1) 127/200

2) 25/99

3) 23/7

4) 4/5

5) 17/8

Practice Set 2.1 | Q 3.1 | Page 21

Write the following rational numbers in p/q form

0.6 °

Practice Set 2.1 | Q 3.2 | Page 21

Write the following rational numbers in p/q form

0.37

Practice Set 2.1 | Q 3.3 | Page 21

Write the following rational numbers in p/q form

3.17

Practice Set 2.1 | Q 3.4 | Page 21

Write the following rational number in p/q form

15.89

Practice Set 2.1 | Q 3.5 | Page 21

Write the following rational numbers in p/q form

2.514

#### Chapter 2: Real Numbers Exercise Practice Set 2.2 solutions [Page 25]

Practice Set 2.2 | Q 1 | Page 25

Show that 4sqrt2 is a rational number.

Practice Set 2.2 | Q 2 | Page 25

Prove that 3 +sqrt 5  is an irrational number.

Practice Set 2.2 | Q 3 | Page 25

Represent the numbers sqrt 5 and sqrt 10 on a number line.

Practice Set 2.2 | Q 4 | Page 25

Write any three rational numbers between the two numbers given below.

1) 0.3 and -0.5

2) -2.3 and -2.33

3) 5.2 and 5.3

4) -4.5 and -4.6

#### Chapter 2: Real Numbers Exercise Practice Set 2.3, Practice set 2.3 solutions [Page 30]

Practice Set 2.3 | Q 1.1 | Page 30

State the order of the surd given below.
root (3)(7)

Practice Set 2.3 | Q 1.2 | Page 30

State the order of the surd given below.

5 sqrt 12

Practice Set 2.3 | Q 1.3 | Page 30

State the order of the surd given below.

root (4)(10)

Practice Set 2.3 | Q 1.4 | Page 30

State the order of the surd given below.

sqrt 39

Practice Set 2.3 | Q 1.5 | Page 30

State the order of the surd given below.

root (3)(18)

Practice Set 2.3 | Q 2.1 | Page 30

State which of the following are surd. Justify.

root (3)(51)

Practice Set 2.3 | Q 2.2 | Page 30

State which of the following are surd. Justify.

root (4)(16)

Practice Set 2.3 | Q 2.3 | Page 30

State which of the following are surd. Justify.

root (5)(81)

Practice Set 2.3 | Q 2.4 | Page 30

State which of the following are surd. Justify.

sqrt 256

Practice Set 2.3 | Q 2.5 | Page 30

State which of the following are surd. Justify.

root (3)(64)

Practice Set 2.3 | Q 2.6 | Page 30

State which of the following are surd.Justify.

sqrt (22/7)

Practice Set 2.3 | Q 3.1 | Page 30

Classify the given pair of surds into like surd and unlike surd.

sqrt 52 , 5 sqrt13

Practice Set 2.3 | Q 3.2 | Page 30

Classify the given pair of surds into like surd and unlike surd.

sqrt 68 , 5 sqrt3

Practice Set 2.3 | Q 3.3 | Page 30

Classify the given pair of surds into like surd and unlike surd.

4 sqrt 18 , 7 sqrt 2

Practice Set 2.3 | Q 3.4 | Page 30

Classify the given pair of surds into like surd and unlike surd.

19 sqrt 12 , 6 sqrt 3

Practice Set 2.3 | Q 3.5 | Page 30

Classify the given pair of surds into like surd and unlike surd.

5 sqrt 22 , 7 sqrt 33

Practice Set 2.3 | Q 3.6 | Page 30

Classify the Given Pair of Surds into like Surd and Unlike Surd.

5sqrt 5, sqrt 75

Practice Set 2.3 | Q 4 | Page 30

Simplify the following surds.

1) sqrt 27

2) sqrt 50

3) sqrt 250

4) sqrt 112

5) sqrt 168

Practice Set 2.3 | Q 5.1 | Page 30

Compare the following pair of surd.

7sqrt2 , 5 sqrt 3

Practice Set 2.3 | Q 5.2 | Page 30

Compare the following pair of surd.

sqrt 247 , sqrt 274

Practice Set 2.3 | Q 5.3 | Page 30

Compare the following pair of surd.

2sqrt 7 , sqrt 28

Practice Set 2.3 | Q 5.4 | Page 30

Compare the following pair of surd.

5 sqrt 5 , 7 sqrt 2

Practice Set 2.3 | Q 5.5 | Page 30

Compare the following pair of surd.

4 sqrt 42 , 9 sqrt 2

Practice Set 2.3 | Q 5.6 | Page 30

Compare the following pair of surd.

5 sqrt 3 , 9

Practice Set 2.3 | Q 5.7 | Page 30

Compare the following pair of surd.

7 , 2 sqrt 5

Practice Set 2.3 | Q 6.1 | Page 30

Simplify.

5 sqrt 3 + 8 sqrt 3

Practice Set 2.3 | Q 6.2 | Page 30

Simplify.

9 sqrt 5 - 4 sqrt 5 + sqrt 125

Practice Set 2.3 | Q 6.3 | Page 30

Simplify.

7 sqrt 48 - sqrt 27 - sqrt 3

Practice Set 2.3 | Q 6.4 | Page 30

Simplify.

sqrt 7 - 3/5 sqrt 7 + 2 sqrt 7

Practice Set 2.3 | Q 7.1 | Page 30

Multiply and write the answer in the simplest form.

3 sqrt 12 xx sqrt 18

Practice Set 2.3 | Q 7.2 | Page 30

Multiply and write the answer in the simplest form.

3sqrt 12 xx 7 sqrt 15

Practice Set 2.3 | Q 7.3 | Page 30

Multiply and write the answer in the simplest form.

3sqrt8 xx sqrt5

Practice Set 2.3 | Q 7.4 | Page 30

Multiply and write the answer in the simplest form.

5 sqrt 8 xx 2 sqrt 8

Practice Set 2.3 | Q 8.1 | Page 30

Divide, and write the answer in simplest form.

sqrt98 ÷ sqrt 2

Practice Set 2.3 | Q 8.2 | Page 30

Divide, and write the answer in simplest form.

sqrt 125 ÷ sqrt 50

Practice Set 2.3 | Q 8.3 | Page 30

Divide, and write the answer in simplest form.

sqrt 54 ÷ sqrt 27

Practice Set 2.3 | Q 8.4 | Page 30

Divide, and write the answer in simplest form.

sqrt 310 ÷ sqrt 5

Practice Set 2.3 | Q 9.1 | Page 30

Rationalize the denominator.

3 /sqrt5

Practice set 2.3 | Q 9.2 | Page 30

Rationalize the denominator.

1/sqrt14

Practice Set 2.3 | Q 9.3 | Page 30

Rationalize the denominator.

5/sqrt 7

Practice Set 2.3 | Q 9.4 | Page 30

Rationalize the denominator.

6/(9sqrt 3)

Practice Set 2.3 | Q 9.5 | Page 30

Rationalize the denominator.

11 / sqrt 3

#### Chapter 2: Real Numbers Exercise Practice Set 2.4 solutions [Page 32]

Practice Set 2.4 | Q 1.1 | Page 32

Multiply
sqrt3 (sqrt 7 - sqrt 3)

Practice Set 2.4 | Q 1.2 | Page 32

Multiply the following surd.

(sqrt 5 - sqrt 7) sqrt 2

Practice Set 2.4 | Q 1.3 | Page 32

Multiply

(3sqrt2 - sqrt 3)  (4sqrt3 - sqrt 2)

Practice Set 2.4 | Q 2.1 | Page 32

Rationalize the denominator.

1/(sqrt 7 + sqrt 2)

Practice Set 2.4 | Q 2.2 | Page 32

Rationalize the denominator.

3/(2 sqrt 5 - 3 sqrt 2)

Practice Set 2.4 | Q 2.3 | Page 32

Rationalize the denominator.

4/(7+ 4 sqrt3)

Practice Set 2.4 | Q 2.4 | Page 32

Rationalize the denominator.

(sqrt 5 - sqrt 3)/(sqrt 5 + sqrt 3)

#### Chapter 2: Real Numbers Exercise Practice Set 2.5 solutions [Page 33]

Practice Set 2.5 | Q 1.1 | Page 33

Find the value.

| 15 - 2 |

Practice Set 2.5 | Q 1.2 | Page 33

Find the value.

| 4 - 9 |

Practice Set 2.5 | Q 1.3 | Page 33

Find the value.

|7| xx |-4|

Practice Set 2.5 | Q 2.1 | Page 33

Solve.

|3x - 5| = 1

Practice Set 2.5 | Q 2.2 | Page 33

Solve.

|7 - 2x | = 5

Practice Set 2.5 | Q 2.3 | Page 33

Solve.

|(8 - x)/2| = 5

Practice Set 2.5 | Q 2.4 | Page 33

Solve.

|5 + x/ 4| = 5

#### Chapter 2: Real Numbers Exercise Problem Set 2, Problem set 2, Problem Set2 solutions [Pages 34 - 355]

Problem Set 2 | Q 1.01 | Page 34

Choose the correct alternative answer for the question given below.

Which one of the following is an irrational number ?

• sqrt (16/25)

• sqrt 5

• 3/9

• sqrt 196

Problem Set 2 | Q 1.02 | Page 34

Choose the correct alternative answer for the question given below.

Which of the following is an irrational number?

• 0.17

• 1.513

• 0.2746

• 0.101001000.....

Problem Set 2 | Q 1.03 | Page 34

Choose the correct alternative answer for the question given below.

Decimal expansion of which of the following is non-terminating recurring ?

• 2/5

• 3/16

• 3/11

• 137/25

Problem Set 2 | Q 1.04 | Page 34

Choose the correct alternative answer for the questions given below.
Every point on the number line represent, which of the following numbers?

• Natural numbers

• Irrational numbers

• Rational numbers

• Real numbers.

Problem Set 2 | Q 1.05 | Page 34

Choose the correct alternative answer for the questions given below.

The number 0.4 in p/q   form is .....

• 4/9

• 40/9

• 3.6/9

• 36/9

Problem Set 2 | Q 1.06 | Page 34

Choose the correct alternative answer for the questions given below.

What is sqrt n , if n is not a perfect square number ?

• Natural number

• Rational number

• Irrational number

• Options A, B, C all are correct.

Problem Set 2 | Q 1.07 | Page 34

Choose the correct alternative answer for the questions given below.

Which of the following is not a surd ?

• sqrt 7

• root (3)(17)

• root (3)(64)

• sqrt 193

Problem Set 2 | Q 1.08 | Page 34

Choose the correct alternative answer for the questions given below.

What is the order of the surd root (3)sqrt (5) ?

• 3

• 2

• 6

• 5

Problem Set 2 | Q 1.09 | Page 34

Choose the correct alternative answer for the questions given below.

Which one is the conjugate pair of 2 sqrt 5 + sqrt 3?

• -2sqrt5 + sqrt 3

• -2sqrt 5 - sqrt 3

• 2 sqrt 3 - sqrt 5

• sqrt 3 + 2 sqrt 5

Problem Set 2 | Q 1.1 | Page 34

Choose the correct alternative answer for the questions given below.

The value of |12 - (13 + 7) xx 4| is ...........

• -68

• 68

• -32

• 32

Problem Set 2 | Q 2.1 | Page 35

Write the following numbers in p / q form.

0.555

Problem Set 2 | Q 2.2 | Page 35

Write the following numbers in p/q form.

29.568

Problem Set 2 | Q 2.3 | Page 35

Write the following numbers in p/q form.

9.315315...

Problem Set 2 | Q 2.4 | Page 35

Write the following numbers in p/q form.

357.417417...

Problem Set 2 | Q 2.5 | Page 35

Write the following numbers in p /q form.

30.219

Problem Set 2 | Q 3.1 | Page 35

Write the following number in its decimal form.

-5/7

Problem Set 2 | Q 3.2 | Page 35

Write the following number in its decimal form.

9/11

Problem Set 2 | Q 3.3 | Page 35

Write the following number in its decimal form.

sqrt 5

Problem Set 2 | Q 3.4 | Page 35

Write the following number in its decimal form.

121/13

Problem Set 2 | Q 3.5 | Page 35

Write the following number in its decimal form.

29/8

Problem Set 2 | Q 4 | Page 35

Show that 5 +sqrt 7  is an irrational number.

Problem Set 2 | Q 5.1 | Page 35

Write the following surd in simplest form.

3/4 sqrt 8

Problem Set 2 | Q 5.2 | Page 35

Write the following surd in simplest form.

-5/9 sqrt 45

Problem Set 2 | Q 6.1 | Page 35

Write the simplest form of rationalising factor for the given surd.

sqrt 32

Problem Set 2 | Q 6.2 | Page 35

Write the simplest form of rationalising factor for the given surd.

sqrt 50

Problem Set 2 | Q 6.3 | Page 35

Write the simplest form of rationalising factor for the given surd.

sqrt 27

Problem set 2 | Q 6.4 | Page 35

Write the simplest form of rationalising factor for the given surd.

3/5 sqrt 10

Problem Set 2 | Q 6.5 | Page 35

Write the simplest form of rationalising factor for the given surd.

3 sqrt 72

Problem Set 2 | Q 6.6 | Page 35

Write the simplest form of rationalising factor for the given surd.

4 sqrt 11

Problem Set 2 | Q 7.1 | Page 35

Simplify.

4/7 sqrt 147 + 3/8 sqrt 192 - 1/5 sqrt 75

Problem Set 2 | Q 7.2 | Page 35

Simplify. 5sqrt 3 + 2 sqrt 27 +1/sqrt3

Problem Set 2 | Q 7.3 | Page 35

Simplify. sqrt 216 - 5 sqrt 6 +sqrt 294 -3/sqrt6

Problem Set2 | Q 7.4 | Page 35

Simplify.  4 sqrt 12 - sqrt 75 - 7 sqrt 48

Problem Set 2 | Q 7.5 | Page 35

Simplify. 2 sqrt 48 - sqrt 75 - 1/ sqrt 3

Problem Set 2 | Q 8.1 | Page 35

Rationalize the denominator.

1/sqrt5

Problem set 2 | Q 8.2 | Page 35

Rationalize the denominator.

2/(3 sqrt 7)

Problem Set 2 | Q 8.3 | Page 35

Rationalize the denominator.

1/(sqrt 3 - sqrt 2)

Problem Set 2 | Q 8.4 | Page 35

Rationalize the denominator.

1/(3 sqrt 5 + 2 sqrt 2)

Problem Set 2 | Q 8.5 | Page 355

Rationalize the denominator.

12/(4sqrt3 - sqrt 2)

## Chapter 2: Real Numbers

Practice Set 2.1Practice Set 2.2Practice Set 2.3Practice set 2.3Practice Set 2.4Practice Set 2.5Problem Set 2Problem set 2Problem Set2

## Balbharati solutions for Class 9 Algebra chapter 2 - Real Numbers

Balbharati solutions for Class 9 chapter 2 (Real Numbers) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Balbharati Class 9 Mathematics 1 Algebra solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com are providing such solutions so that students can prepare for written exams. Balbharati textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 9 Algebra chapter 2 Real Numbers are Rationalization of the Denominator, Binomial Quadratic Surd, Rationalization of Surd, Operation on like Surds, Forms of Surds, Concept of Surds, Properties of Order Relation on Real Numbers, Decimal Form of Irrational Numbers, Rational and Irrational Numbers, Properties of Real Numbers, Concept of Real Numbers.

Using Balbharati Class 9 solutions Real Numbers exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Balbharati Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board Class 9 prefer Balbharati Textbook Solutions to score more in exam.

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