Maharashtra Board Class 9 Math Chapter 2 Real Numbers Solution

Maharashtra Board Class 9 Math Solution Chapter 2 – Real Numbers

Balbharati Maharashtra Board Class 9 Math Solution Chapter 2: Real Numbers. Marathi or English Medium Students of Class 9 get here Real Numbers full Exercise Solution.

Std

Maharashtra Class 9

Subject

Math Solution

Chapter

Real Numbers


Practice set 2.1

 

Practice Set 2.2

(i) Show that 4√2 be irrational number.

Therefore, 4√2 can be expressed in the from p/q where p and q are integers and q ≠ o

Therefore, 4≠2 = p/q

=> √2 = p/4q

Therefore, p/4q is rational number

Therefore, √2 is also a rational number which is a contradiction due to the wrong assumption that 4√2 is rational

Therefore, 4√2 is irrational.

 

(2) Prove that 3 + √5 is an irrational number

A: Let, 3 + √5 be rational

Therefore, 3 + √5 can be expressed in the form p/q where p and q are integers and q ≠ o

Therefore, 3 + √5 = p/q

=> √5 = p/q – 3

Because, p/q – 3 is rational numbers

Therefore, √5 should also be rational which is contradiction due to the assumption that 3 + √5 is rational

Therefore, 3+√5 is irrational.

(3) Represent the numbers √5 and √10 on a number line

A: Because representation on a number line :

Because, √4 = 2 and √9 = 3 and √5 lies between √4 and √9, so, √5 lies 2 and 3.

We take OA = 2 units and draw AB = 1 unit perpendicular to the number line and join OB. With O as centre and OB as length we cut are on the number line. The point at which the fare cuts the numbers line gives √5 on the numbers line.

√10 representation on a number line

Because, √9 = 3 and √16 = 4 and √10 lies between √4 and √16 i.e., √10 lies between 3 and 4.

We take OA = 3 units and draw AB = 1 unit perpendicular to the number line and join OB. With O as centre and OB as length we cut are on the number line. The point at which the are cuts the number line gives √10 on the number line.

(4) Write any three rational numbers between the two numbers given below.

(i) 0.3 and -0.5

A: -0.3, -0.1, 0.1

 

(ii) -2.3 and -2.33

A: -2.31, -2.32, -2.312

 

(iii) 5.2 and 5.3

A: 5.21, 5.25, 5.29

 

(iv)- 4.5 and -4.6

A: – 4.52, -4.56, – 4.57

 

Practice set 2.3

 

(1) State the order of the surds given below.

(i) 3√7

(ii) 5√12

(iii) 4√10

(iv) √39

(v) 3√18

A: (i) 3

(ii) 2

(iii) 4

(iv) 2

(v) 3

 

(2) State which of the following are surds justify

(i) 3√51

A: Here a = 51, order of word, n = 4

But 3rd root of 51 is not a rational number.

Therefore, 3√51 is an irrational number

Therefore, 3√51 is a surd.

 

(ii) 4√16

A: Here a = 16, n = 4

Let, 16 = p4 and we know 4th power 2 gives 16

Therefore, 16 = 24 => 4√16 = 2 which is a rational number

Therefore, 4√16 is not surd.

 

(iii) 5√81

A: Here a = 81, order of surd, n = 5 but, 5th root of 81 is not a rational numbers

Therefore, 5√81 is an irrational numbers

Therefore, 5√81 a surd

 

(iv) √256

A: Here, a = 256 and n = 2

Let, 256 = p2 and we know that 256 = 162

Therefore, 256 = 162 => √256 = 16 which is a rational number

Therefore, √256 is not a surd

 

(v) 3√64

A: Here a = 64 and n = 3 but, 3rd root of 64 is 4

Let, 64 = p3 and we know that 64 = 43

Therefore, 64 = 43 => 3√64 = 4 which is a rational number

Therefore, 3√64 is not surd

 

(vi) √22/7

A: Here, a = 22/7 and n = 2

But square root of 22/7 is not a rational number

Therefore, √22/7 is an irrational number

Therefore, √22/7 is a surd

 

(3) Classify the given pair of surds into surds and unlike surds

(i)  √52, 5√13

A: Here, √52 = √4 x 13 = √4 √13 = 2√13

Because, Both order and radicand of 2√13 and 5√13 are same

Therefore, √52 and 5√13 are like surds.

(8) Divided and write answer in simplest form:

 

(i) √98 ÷ √2

A: √98 ÷ √2

= √98/2

= √49

= 7

 

(ii) √125 ÷ √50

A √125 ÷ √50

= √125/50

= √5/2

= √5/√2

 

(iii) √54 ÷ √27

A: √54 ÷ √27

= √54/27

= √2

 

(iv) √310 ÷ √5

√310 ÷ √5

= √310/5

= √62

 

(9) Rationalize the denominator

 

(i) 3/√5

A: 3/√5 = 3/√5 x √5/√5 = 3√5/5

 

(ii) 1/√14

A: Multiplying and dividing √14

1/√14 = 1/√14 x √14/√14 = √14/14

 

(iii) 5/√7

= Multiplying and dividing by √7

5/√7 = 5/√7 x √7/√7

= 5√7/7

 

(iv) 6/9√3

A: Multiplying and dividing by √3

6/9√3 = 6/9√3 x √3/√3 = 6√3/9 x3 = 2√3/9

 

(v) 11/√3

A: Multiplying and dividing by √3

11/√3 = 11/√3 x √3/√3 = 11√3/3

 

Practice set 2.4

(i) Multiply

(i) √3(√7 – √3)

A: √3 (√7 – √3)

= √3 x √7 – √3 x √3

=21-3

= 3 + √21

 

(ii) (√5-√7) √2

A: (√5-√7) √2

= √5 x √2 – √7 x √2

= √10 – √14

 

(iii) (3√2 – √3) (4√3 – √2)

A: (3√2 – √3) (4√3 – √2) = 3√2(4√3 – √2) – √3 (4√3-√2)

= 3√2 x 4√3 – 3√2 x √2 – √3 x 4√3 + √3 + √3 x √2

= 12√6 – 3 x 2 – 4 x 3 + √6

= 16√6 -6 -12

= 13√6 – 18 = -18 + 13√6

 

(2) Rationalize the denominator

 

(i) 1/√7 + √2

A: Multiplying and dividing by √7 – √2

1/√7 + √2

= 1/√7 + √2 x √7 – √2/√7 – √2

= √7 – √2/√72 – √22

= √7 – √2/7-2

= √7 – √2/5

 

Practice set 2.5

 

(i) Find the value

(i) |15-2|

A: |15-2|

= |13|

= 13

 

(ii) |4-9|

A: |4-9|

= |-5|

= 5

 

(iii) 17| x |-4|

A: 17| x |-4|

= 7 x 4

= 28

 

(2) Solve:

 

(i) |3x – 5| = 1

A: |3x – 5| = 1

i.e., 3x – 5 = +- 1

Therefore, 3x – 5 = 1

=> 3x = 6

=> x = 2

Or, 3x – 5 = 1

Or, => 3x = 4

Or, => x = 4/3

 

(ii) |7 – 2x| = 5

A: |7-2x| = 5

i.e., 7-2x = +-5

Therefore, 7-2x = 5

=> 2x = 7-5

=> x = 2/2

=> x = 1

Or, 7 – 2x = -5

Or, => 2x = 7+5

Or, => x = 12/6

O=> x = 6

 

(iii) | 8 – x/2| = 5

A: |8 – x/2| = 5

i.e., 8 – x/2 = +- 5

Therefore, 8 – x/2 = 5

=> 8 – x = 10

=> x = 8-10

=> x = -2

Or, 8 – x/2 = -5

Or, => 8 – x = -10

Or => x = 8 + 10

Or, x = 18

 

(iv) |5 + x/4| = 5

A: |5 + x/4| = 5

i.e., 5 + x/4 = +-5

Therefore, 5 + x/4 = 5

=> x/4 = 5 – 5

=> x = 0

Or, 5 + x/4 = -5

Or, => x/4 = -5 -5

Or => x = -10 x 4 = -40

 

Problem set 2

(i) Choose the correct alternative answer for the questions given below.

(i) Which one of the following is an irrational number?

(A) √16/25

(B) √5

(C) 3/9

(D) √196

=A: (B) √5

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

(A) 2/5

(B) 3/16

(C) 3/11

(D) 137/25

A: (C) 3/11

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

(A) Natural numbers

(b) Irrational numbers

(C) Rational numbers

(D) Real numbers

A: (D) Real numbers.

 

Here is your solution of Maharashtra Board Class 9 Math Chapter 2 Real Numbers 

Dear Student, I appreciate your efforts and hard work that you all had put in. Thank you for being concerned with us and I wish you for your continued success.

 

Updated: July 19, 2021 — 1:55 pm

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