Class 8 RD Sharma Mathematics Solutions Chapter 3 Squares and Square Roots Exercise 3.8 (original) (raw)

Last Updated : 23 Jul, 2025

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

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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.