# Class 8 RD Sharma Solutions – Chapter 3 Squares and Square Roots – 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 Long Division Method to find 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 √12×12 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) 196/75We 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:

= √(14×14) / √(3x5x5) = 14/5√3

5√3 is equal to 5×1.732

= 8.66 = 1.617

(ii) 400/63We 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

= √(20×20)/√(3x3x7)

= 20 / 3√7

3√7 is equal to 3×2.646

= 7.938

= 2.520

(iii) 150/7We 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) 256/5We 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:

= √(16×16) / √(5)

= 16 / √5

√5 is equal to 2.236

= 7.155

(v) 27/50We 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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