#### Chapters

#### Balbharati Balbharati Class 9 Mathematics 1 Algebra

## Chapter 2: Real Numbers

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

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

`13/5`

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

`2/11`

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

`29/16`

`17/125`

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

`11/6`

Write the following rational numbers in decimal form.

1) `127/200`

2) `25/99`

3) `23/7`

4) `4/5`

5) `17/8`

Write the following rational numbers in `p/q` form

0.6 °

Write the following rational numbers in `p/q` form

0.37

Write the following rational numbers in `p/q` form

3.17

Write the following rational number in `p/q` form

15.89

Write the following rational numbers in `p/q` form

2.514

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

Show that `4sqrt2` is a rational number.

Prove that 3 +`sqrt 5` is an irrational number.

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

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]

State the order of the surd given below.

`root (3)(7)`

State the order of the surd given below.

`5 sqrt 12`

State the order of the surd given below.

`root (4)(10)`

State the order of the surd given below.

`sqrt 39`

State the order of the surd given below.

`root (3)(18)`

State which of the following are surd. Justify.

`root (3)(51)`

State which of the following are surd. Justify.

`root (4)(16)`

State which of the following are surd. Justify.

`root (5)(81)`

State which of the following are surd. Justify.

`sqrt 256`

State which of the following are surd. Justify.

`root (3)(64)`

State which of the following are surd.Justify.

`sqrt (22/7)`

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

`sqrt 52 , 5 sqrt13`

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

`sqrt 68 , 5 sqrt3`

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

`4 sqrt 18 , 7 sqrt 2`

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

`19 sqrt 12 , 6 sqrt 3`

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

`5 sqrt 22 , 7 sqrt 33`

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

`5sqrt 5, sqrt 75`

Simplify the following surds.

1) `sqrt 27`

2) `sqrt 50`

3) `sqrt 250`

4) `sqrt 112`

5) `sqrt 168`

Compare the following pair of surd.

`7sqrt2 , 5 sqrt 3`

Compare the following pair of surd.

`sqrt 247 , sqrt 274`

Compare the following pair of surd.

`2sqrt 7 , sqrt 28`

Compare the following pair of surd.

`5 sqrt 5 , 7 sqrt 2`

Compare the following pair of surd.

`4 sqrt 42 , 9 sqrt 2`

Compare the following pair of surd.

`5 sqrt 3 , 9`

Compare the following pair of surd.

`7 , 2 sqrt 5`

Simplify.

`5 sqrt 3 + 8 sqrt 3`

Simplify.

`9 sqrt 5 - 4 sqrt 5 + sqrt 125`

Simplify.

`7 sqrt 48 - sqrt 27 - sqrt 3`

Simplify.

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

Multiply and write the answer in the simplest form.

`3 sqrt 12 xx sqrt 18`

Multiply and write the answer in the simplest form.

`3sqrt 12 xx 7 sqrt 15`

Multiply and write the answer in the simplest form.

`3sqrt8 xx sqrt5`

Multiply and write the answer in the simplest form.

`5 sqrt 8 xx 2 sqrt 8`

Divide, and write the answer in simplest form.

`sqrt98 ÷ sqrt 2`

Divide, and write the answer in simplest form.

`sqrt 125 ÷ sqrt 50`

Divide, and write the answer in simplest form.

`sqrt 54 ÷ sqrt 27`

Divide, and write the answer in simplest form.

`sqrt 310 ÷ sqrt 5`

Rationalize the denominator.

`3 /sqrt5`

Rationalize the denominator.

`1/sqrt14`

Rationalize the denominator.

`5/sqrt 7`

Rationalize the denominator.

`6/(9sqrt 3)`

Rationalize the denominator.

`11 / sqrt 3`

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

Multiply

`sqrt3 (sqrt 7 - sqrt 3)`

Multiply the following surd.

`(sqrt 5 - sqrt 7) sqrt 2`

Multiply

`(3sqrt2 - sqrt 3) (4sqrt3 - sqrt 2)`

Rationalize the denominator.

`1/(sqrt 7 + sqrt 2)`

Rationalize the denominator.

`3/(2 sqrt 5 - 3 sqrt 2)`

Rationalize the denominator.

`4/(7+ 4 sqrt3)`

Rationalize the denominator.

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

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

Find the value.

`| 15 - 2 | `

Find the value.

`| 4 - 9 |`

Find the value.

`|7| xx |-4|`

Solve.

`|3x - 5| = 1`

Solve.

`|7 - 2x | = 5`

Solve.

`|(8 - x)/2| = 5`

Solve.

`|5 + x/ 4| = 5`

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

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`

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.....

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`

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.

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`

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.

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`

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

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`

Choose the correct alternative answer for the questions given below.

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

-68

68

-32

32

Write the following numbers in `p / q` form.

0.555

Write the following numbers in `p/q` form.

29.568

Write the following numbers in `p/q` form.

`9.315315...`

Write the following numbers in `p/q` form.

357.417417...

Write the following numbers in `p /q` form.

30.219

Write the following number in its decimal form.

`-5/7`

Write the following number in its decimal form.

`9/11`

Write the following number in its decimal form.

`sqrt 5`

Write the following number in its decimal form.

`121/13`

Write the following number in its decimal form.

`29/8`

Show that `5 +sqrt 7` is an irrational number.

Write the following surd in simplest form.

`3/4 sqrt 8`

Write the following surd in simplest form.

`-5/9 sqrt 45`

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

`sqrt 32`

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

`sqrt 50`

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

`sqrt 27`

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

`3/5 sqrt 10`

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

`3 sqrt 72`

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

`4 sqrt 11`

Simplify.

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

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

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

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

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

Rationalize the denominator.

`1/sqrt5`

Rationalize the denominator.

`2/(3 sqrt 7)`

Rationalize the denominator.

`1/(sqrt 3 - sqrt 2)`

Rationalize the denominator.

`1/(3 sqrt 5 + 2 sqrt 2)`

Rationalize the denominator.

`12/(4sqrt3 - sqrt 2) `

## Chapter 2: Real Numbers

#### Balbharati Balbharati Class 9 Mathematics 1 Algebra

#### Textbook solutions for Class 9

## 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.

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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.

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