Class 8 RD Sharma Mathematics Solutions - Chapter 3 Squares and Square Roots - Exercise 3.8

In Chapter 3 of RD Sharma's Class 8 Mathematics textbook students delve into the concepts of the squares and square roots. Exercise 3.8 specifically focuses on applying these concepts to solve various problems helping students reinforce their understanding through practical examples. This exercise is crucial for building a strong foundation in algebra and geometry as squares and square roots are frequently encountered in higher mathematics.

Squares and Square Roots

The Squares of a number refer to the product of the number multiplied by itself. For example: the square of 5 is 5×5=25. On the other hand, the square root of a number is a value that when multiplied by itself gives the original number. For instance, the square root of 25 is 5 since 5×5=25. These concepts are foundational in understanding the various mathematical principles and are used in solving quadratic equations, calculating areas, and more.

Class 8 RD Sharma Mathematics Solutions - Exercise 3.8

Question 1. Find the square root of each of the following correct to three places of decimal.

i) 5                                                                                                                                                                                                                                                  

Solution: We will use the Long Division Method to find the square root of 5    

Square root of 5 is 2.2360

ii) 7

Solution: We will use Long Division Method to find square root of 7                                                                                                                                                                       

Square root of 7 is 2.6457

iii) 17

Solution: We will use Long Division Method to find square root of 17                                                                                                                                                                  

Square root of 17 is 4.123

iv) 20 

Solution: We will use Long Division Method to find square root of 20

Square root of 20 is 4.4721

v) 66

Solution: We will use Long Division Method to find square root of 66

Square root of 66 is 8.1240

vi) 427

Solution: We will use Long Division Method to find square root 427

Square root of 427 is 20.6639

vii) 1.7

Solution: We will use Long Division Method to find square root of 1.7

Square root of 1.7 is 1.3038

viii) 23.1

Solution: We will use Long Division Method to find square root of 23.1

Square root of 23.1 is 4.8062

ix) 2.5 

Solution: We will use Long Division Method to find square root of 2.5

Square root of 2.5 is 1.5811

x) 237.615

Solution: We will use Long Division Method to find square root of 237.615

Square root of 237.615 is 15.4147

xi) 15.3215

Solution: We will use Long Division Method to find square root of 15.3215

Square root of 15.3215 is 3.9142

xii) 0.9

Solution: We will use Long Division Method to find square root of 0.9

Square root of 0.9 is 0.9486

xiii) 0.1

Solution: We will use Long Division Method to find square root of 0.1

Square root of 0.1 is 0.3162

xiv) 0.016

Solution: We will use Long Division Method to find square root of 0.016

Square root of 0.016 is 0.1264

xv) 0.00064

Solution: We will use Long Division Method to find square root of 0.00064

Square root of 0.00064 is 0.0252         

xvi) 0.019

Solution: We will use Long Division Method to find square root of 0.019

Square root of 0.019 is 0.1378                                                  

xvii) 7/8

Solution:  We will use Long Division Method to find square root of 7/8

Square root of 7/8 is 0.9354

xviii) 5/12

Solution: We will use Long Division Method to find square root of 5/12

Square root of 5/12 is 0.6454

xix) 2 ½

Solution: We will use Long Division Method to find square root of 2 ½

Square root of 2 ½ is 1.5811

xx) 287 5⁄8

Solution: We will use Long Division Method to find square root of 287 5⁄8

Square root of 287 5⁄8 is 16.9593

Question 2. Find the square root of 12.0068 correct to four decimal places.

Solution: We will use Long Division Method to find square root of 12.0068 correct to four decimal place

The square root of 12.0068 correct to four decimal place is 3.46508

Question 3. Find the square root of 11 correct to five decimal places.

Solution: We will use Long Division Method to find square root of 11 up to five decimal place

The square root of 11 correct to five decimal place is 3.316624

Question 4. Give that: √2 = 1.414, √3 = 1.732, √5 = 2.236 and √7 = 2.646, Evaluate each of the following :   

(i) √(144/7)    (ii) √(2500/3)

Solution:

(i) √(144/7) 

We can write √144 as √12x12 and we will calculate square root of √7 

= 2.646 = √(12×12)/ √7 

= 12/ 2.646 = 4.535

(ii) √(2500/3) 

We will find factor of √2500 = √2x2x5x5x5x5, which is equal to 50 and we will calculate square root of √3                            

which is equal to 1.732 = 50/1.732 = 28.867

Question 5. Given that √2 = 1.414, √3 = 1.732, √5 = 2.236 and √7 = 2.646 find the square roots of the following : 

(i) 196/75     (ii) 400/63     (iii) 150/7     (iv) 256/5    (v) 27/50

Solution: 

(i) 196/75   

We have to calculate square root of √(196/75) , we can write it as √(196) / √(75)                                                                     

Now find the factors of both numerator and denominator, we can write it as: 

= √(14x14) / √(3x5x5) = 14/5√3 

5√3 is equal to 5x1.732 

= 8.66 = 1.617              

(ii) 400/63 

We have to calculate square root of √(400/63), we can write it as √(400)/√(63)                                                                      

Now find the factors of both numerator and denominator, we can write it as

= √(20x20)/√(3x3x7) 

= 20 / 3√7 

3√7 is equal to 3x2.646 

= 7.938 

= 2.520

(iii) 150/7 

We have to calculate square root of √(150/7), we can write it as √(150) / √(7)                                                                          

Now find the factors of both numerator and denominator, we can write it as: 

= √(3x5x5x2)/√(7) = 5x√3x√2 / √7 

5x√3x√2 is equal to 5 x 1.732 x 1.414 

= 12.245 

= 12.245 / 2.646 

= 4.628

(iv) 256/5 

We have to calculate square root of √(256/5), we can write it as √(256) / √(5) 

Now find the factors of both numerator and denominator, we can write it as:    

= √(16x16) / √(5)  

= 16 / √5 

√5 is equal to 2.236 

= 7.155

(v) 27/50 

We have to calculate square root of √(27/50), we can write it as √(27) / √(50) 

Now find the factors of both numerator and denominator, we can write it as: 

= √(3x3x3) / √(2x5x5) = 3√3 / 5√2 

3√3 is equal to 5.196 and 5√2 = 7.07

= 0.735

Also Read:

• Square and Square roots
• Class 8 RD Sharma Mathematics Solutions - Chapter 3 Squares and Square Roots - Exercise 3.2 | Set 1
• Class 8 RD Sharma Mathematics Solutions - Chapter 3 Squares and Square Roots - Exercise 3.5
• Class 8 RD Sharma Mathematics Solutions - Chapter 3 Squares and Square Roots - Exercise 3.6

Conclusion

Exercise 3.8 in Chapter 3 of RD Sharma's Class 8 Mathematics textbook provides students with the variety of problems that enhance their understanding of the squares and square roots. By practicing these problems students can build confidence in their ability to the handle more complex mathematical concepts in the future.