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Maharashtra State BoardSSC (English Medium) 9th Standard

Balbharati solutions for मैथमैटिक्स १ [अंग्रेजी] कक्षा ९ महाराष्ट्र राज्य बोर्ड chapter 2 - Real Numbers [Latest edition]

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Balbharati solutions for मैथमैटिक्स १ [अंग्रेजी] कक्षा ९ महाराष्ट्र राज्य बोर्ड chapter 2 - Real Numbers - Shaalaa.com
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Solutions for Chapter 2: Real Numbers

Below listed, you can find solutions for Chapter 2 of Maharashtra State Board Balbharati for मैथमैटिक्स १ [अंग्रेजी] कक्षा ९ महाराष्ट्र राज्य बोर्ड.


Practice Set 2.1Practice Set 2.2Practice Set 2.3Practice Set 2.4Practice Set 2.5Problem Set 2
Practice Set 2.1 [Page 21]

Balbharati solutions for मैथमैटिक्स १ [अंग्रेजी] कक्षा ९ महाराष्ट्र राज्य बोर्ड 2 Real Numbers Practice Set 2.1 [Page 21]

1. (i)Page 21

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

`13/5`

1. (ii)Page 21

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

`2/11`

1. (iii)Page 21

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

`29/16`

1. (iv)Page 21

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

`17/125`

1. (v)Page 21

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

`11/6`

2. (i)Page 21

Write the following rational number in decimal form.

`127/200`

2. (ii)Page 21

Write the following rational number in decimal form.

`25/99`

2. (iii)Page 21

Write the following rational number in decimal form.

`23/7`

2. (iv)Page 21

Write the following rational number in decimal form.

`4/5`

2. (v)Page 21

Write the following rational number in decimal form.

`17/8`

3. (i)Page 21

Write the following rational numbers in `bb(p/q)` form.

\[\ce{0.\overset{\bullet}{6}}\]

3. (ii)Page 21

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

0.37

3. (iii)Page 21

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

3.17

3. (iv)Page 21

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

15.89

3. (v)Page 21

Write the following rational number in `bb(p/q)` form.

2.514 

Practice Set 2.2 [Page 25]

Balbharati solutions for मैथमैटिक्स १ [अंग्रेजी] कक्षा ९ महाराष्ट्र राज्य बोर्ड 2 Real Numbers Practice Set 2.2 [Page 25]

(1)Page 25

Show that `4sqrt2` is an irrational number. 

(2)Page 25

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

(3)Page 25

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

(4) (i)Page 25

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

0.3 and -0.5

(4) (ii)Page 25

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

−2.3 and −2.33

(4) (iii)Page 25

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

5.2 and 5.3

(4) (iv)Page 25

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

-4.5 and -4.6

Practice Set 2.3 [Page 30]

Balbharati solutions for मैथमैटिक्स १ [अंग्रेजी] कक्षा ९ महाराष्ट्र राज्य बोर्ड 2 Real Numbers Practice Set 2.3 [Page 30]

(1) (i)Page 30

State the order of the surd given below. 

`root (3)(7)`

(1) (ii)Page 30

State the order of the surd given below.

`5 sqrt 12`

(1) (iii)Page 30

State the order of the surd given below.

`root (4)(10)`

(1) (iv)Page 30

State the order of the surd given below.

`sqrt 39`

(1) (v)Page 30

State the order of the surd given below.

`root (3)(18)`

(2) (i)Page 30

State whether the following number is a surd or not.

`root (3)(51)`

(2) (ii)Page 30

State whether the following number is a surd or not.

`root (4)(16)`

(2) (iii)Page 30

State whether the following number is a surd or not.

`root (5)(81)`

(2) (iv)Page 30

State whether the following number is a surd or not.

`sqrt 256`

(2) (v)Page 30

State whether the following number is a surd or not.

`root (3)(64)`

(2) (vi)Page 30

State whether the following number is a surd or not.

`sqrt (22/7)`

(3) (i)Page 30

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

`sqrt 52, 5 sqrt13`

(3) (ii)Page 30

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

`sqrt 68, 5 sqrt3`

(3) (iii)Page 30

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

`4 sqrt 18 , 7 sqrt 2`

(3) (iv)Page 30

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

`19 sqrt 12 , 6 sqrt 3`

(3) (v)Page 30

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

`5 sqrt 22 , 7 sqrt 33`

(3) (vi)Page 30

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

`5sqrt 5, sqrt 75`

(4) (i)Page 30

Simplify the following surd.

`sqrt 27`

(4) (ii)Page 30

Simplify the following surd.

`sqrt 50`

(4) (iii)Page 30

Simplify the following surd.

`sqrt 250`

(4) (iv)Page 30

Simplify the following surd.

`sqrt 112`

(4) (v)Page 30

Simplify the following surd.

`sqrt 168`

(5) (i)Page 30

Compare the following pair of surd.

`7sqrt2, 5 sqrt 3`

(5) (ii)Page 30

Compare the following pair of surd.

`sqrt 247, sqrt 274`

(5) (iii)Page 30

Compare the following pair of surd.

`2sqrt 7, sqrt 28` 

(5) (iv)Page 30

Compare the following pair of surd.

`5 sqrt 5, 7 sqrt 2`

(5) (v)Page 30

Compare the following pair of surd.

`4 sqrt 42, 9 sqrt 2`

(5) (vi)Page 30

Compare the following pair of surd.

`5 sqrt 3, 9`

(5) (vii)Page 30

Compare the following pair of surd.

`7, 2 sqrt 5`

(6) (i)Page 30

Simplify.

`5 sqrt 3 + 8 sqrt 3`

(6) (ii)Page 30

Simplify.

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

(6) (iii)Page 30

Simplify.

`7 sqrt 48 - sqrt 27 - sqrt 3`

(6) (iv)Page 30

Simplify.

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

(7) (i)Page 30

Multiply and write the answer in the simplest form.

`3 sqrt 12 xx sqrt 18`

(7) (ii)Page 30

Multiply and write the answer in the simplest form.

`3sqrt 12 xx 7 sqrt 15`

(7) (iii)Page 30

Multiply and write the answer in the simplest form.

`3sqrt8 xx sqrt5`

(7) (iv)Page 30

Multiply and write the answer in the simplest form.

`5 sqrt 8 xx 2 sqrt 8`

(8) (i)Page 30

Divide and write the answer in simplest form.

`sqrt98 ÷ sqrt 2`

(8) (ii)Page 30

Divide and write the answer in simplest form.

`sqrt 125 ÷ sqrt 50`

(8) (iii)Page 30

Divide and write the answer in simplest form.

`sqrt 54 ÷ sqrt 27`

(8) (iv)Page 30

Divide and write the answer in simplest form.

`sqrt 310 ÷ sqrt 5`

(9) (i)Page 30

Rationalize the denominator.

`3 /sqrt5`

(9) (ii)Page 30

Rationalize the denominator.

`1/sqrt14`

(9) (iii)Page 30

Rationalize the denominator.

`5/sqrt 7`

(9) (iv)Page 30

Rationalize the denominator.

`6/(9sqrt 3)`

(9) (v)Page 30

Rationalize the denominator.

`11 / sqrt 3`

Practice Set 2.4 [Page 32]

Balbharati solutions for मैथमैटिक्स १ [अंग्रेजी] कक्षा ९ महाराष्ट्र राज्य बोर्ड 2 Real Numbers Practice Set 2.4 [Page 32]

(1) (i)Page 32

Multiply

`sqrt3 (sqrt 7 - sqrt 3)`

(1) (ii)Page 32

Multiply.

`(sqrt 5 - sqrt 7) sqrt 2`

(1) (iii)Page 32

Multiply.

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

(2) (i)Page 32

Rationalize the denominator.

`1/(sqrt 7 + sqrt 2)` 

(2) (ii)Page 32

Rationalize the denominator.

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

(2) (iii)Page 32

Rationalize the denominator.

`4/(7+ 4 sqrt3)`

(2) (iv)Page 32

Rationalize the denominator.

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

Practice Set 2.5 [Page 33]

Balbharati solutions for मैथमैटिक्स १ [अंग्रेजी] कक्षा ९ महाराष्ट्र राज्य बोर्ड 2 Real Numbers Practice Set 2.5 [Page 33]

(1) (i)Page 33

Find the value.

`|15 - 2|`

(1) (ii)Page 33

Find the value.

`|4 - 9|`

(1) (iii)Page 33

Find the value.

`|7| xx |-4|`

(2) (i)Page 33

Solve.

`|3x - 5| = 1` 

(2) (ii)Page 33

Solve.

`|7 - 2x | = 5`

(2) (iii)Page 33

Solve.

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

(2) (iv)Page 33

Solve.

`|5 + x/ 4| = 5`

Problem Set 2 [Pages 34 - 35]

Balbharati solutions for मैथमैटिक्स १ [अंग्रेजी] कक्षा ९ महाराष्ट्र राज्य बोर्ड 2 Real Numbers Problem Set 2 [Pages 34 - 35]

Choose the correct alternative answer for the question given below.

(1) (i)Page 34

Which one of the following is an irrational number?

  • `sqrt (16/25)`

  • `sqrt 5`

  • `3/9`

  • `sqrt 196`

(1) (ii)Page 34

Which of the following is an irrational number?

  • 0.17

  • 1.513 

  • 0.2746 

  • 0.101001000.....

(1) (iii)Page 34

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

  • `2/5`

  • `3/16`

  • `3/11`

  • `137/25`

(1) (iv)Page 34

Every point on the number line represent, which of the following numbers?

  • Natural numbers

  • Irrational numbers 

  • Rational numbers

  • Real numbers

(1) (v)Page 34

The number \[\ce{0.\overset{\bullet}{4}}\] in `p/q`  form is ______.

  • `4/9`

  • `40/9`

  • `3.6/9`

  • `36/9`

(1) (vi)Page 34

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.

(1) (vii)Page 34

Which of the following is not a surd?

  • `sqrt 7`

  • `root (3)(17)`

  • `root (3)(64)`

  • `sqrt 193` 

(1) (viii)Page 34

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

  • 3

  • 2

  • 6

  • 5

(1) (ix)Page 34

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`

(1) (x)Page 34

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

  • -68

  • 68

  • -32

  • 32

(2) (i)Page 35

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

0.555 

(2) (ii)Page 35

Write the following number in `bb("p"/"q")` form.

29.568 

(2) (iii)Page 35

Write the following number in `bb("p"/"q")` form.

9.315315...

(2) (iv)Page 35

Write the following numbers in `bb("p"/"q")` form.

357.417417...

(2) (v)Page 35

Write the following numbers in `bb("p"/"q")` form.

30.219 

(3) (i)Page 35

Write the following number in its decimal form. 

`(-5)/7`

(3) (ii)Page 35

Write the following number in its decimal form.

`9/11`

(3) (iii)Page 35

Write the following number in its decimal form.

`sqrt 5`

(3) (iv)Page 35

Write the following number in its decimal form.

`121/13`

(3) (v)Page 35

Write the following number in its decimal form.

`29/8`

(4)Page 35

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

(5) (i)Page 35

Write the following surd in simplest form.

`3/4 sqrt 8`

(5) (ii)Page 35

Write the following surd in simplest form.

`-5/9 sqrt 45`

(6) (i)Page 35

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

`sqrt 32`

(6) (ii)Page 35

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

`sqrt 50`

(6) (iii)Page 35

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

`sqrt 27`

(6) (iv)Page 35

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

`3/5 sqrt 10`

(6) (v)Page 35

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

`3 sqrt 72`

(6) (vi)Page 35

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

`4 sqrt 11`

(7) (i)Page 35

Simplify. 

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

(7) (ii)Page 35

Simplify.

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

(7) (iii)Page 35

Simplify.

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

(7) (iv)Page 35

Simplify. 

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

(7) (v)Page 35

Simplify.

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

(8) (i)Page 35

Rationalize the denominator.

`1/sqrt5`

(8) (ii)Page 35

Rationalize the denominator.

`2/(3 sqrt 7)`

(8) (iii)Page 35

Rationalize the denominator.

`1/(sqrt 3 - sqrt 2)`

(8) (iv)Page 35

Rationalize the denominator.

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

(8) (v)Page 35

Rationalize the denominator.

`12/(4sqrt3 - sqrt 2)`

Solutions for 2: Real Numbers

Practice Set 2.1Practice Set 2.2Practice Set 2.3Practice Set 2.4Practice Set 2.5Problem Set 2
Balbharati solutions for मैथमैटिक्स १ [अंग्रेजी] कक्षा ९ महाराष्ट्र राज्य बोर्ड chapter 2 - Real Numbers - Shaalaa.com

Balbharati solutions for मैथमैटिक्स १ [अंग्रेजी] कक्षा ९ महाराष्ट्र राज्य बोर्ड chapter 2 - Real Numbers

Shaalaa.com has the Maharashtra State Board Mathematics मैथमैटिक्स १ [अंग्रेजी] कक्षा ९ महाराष्ट्र राज्य बोर्ड Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. Balbharati solutions for Mathematics मैथमैटिक्स १ [अंग्रेजी] कक्षा ९ महाराष्ट्र राज्य बोर्ड Maharashtra State Board 2 (Real Numbers) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. Balbharati textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.

Concepts covered in मैथमैटिक्स १ [अंग्रेजी] कक्षा ९ महाराष्ट्र राज्य बोर्ड chapter 2 Real Numbers are Rational Numbers, Decimal Representation to Identify Irrational Numbers, Properties of Order Relation on Real Numbers, Decimal Representation of Rational Numbers, Simplification of Surds, Absolute Value of Real Numbers, Properties of Rational Numbers, Commutative Property of Rational Numbers, Associative Property of Rational Numbers, Identity of Addition and Multiplication of Rational Numbers, Negative Or Additive Inverse of Rational Numbers, Square Root of Decimal Numbers, Square Root of a Negative Number, Root of Positive Rational Number, Surds, Types of Surds, Comparison of Surds, Operations on Surds, Rationalisation of Surds, Binomial Quadratic Surd, Simplifying an Expression by Rationalization of the Denominator, Concept of Real Numbers.

Using Balbharati मैथमैटिक्स १ [अंग्रेजी] कक्षा ९ महाराष्ट्र राज्य बोर्ड solutions Real Numbers exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in Balbharati Solutions are essential questions that can be asked in the final exam. Maximum Maharashtra State Board मैथमैटिक्स १ [अंग्रेजी] कक्षा ९ महाराष्ट्र राज्य बोर्ड students prefer Balbharati Textbook Solutions to score more in exams.

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