# Frank Learning Maths Class 8 Chapter 3 Squares and Square Roots Exercise 3.1 Solutions

## Frank Learning Maths Class 8 Chapter 3 Squares and Square Roots Exercise 3.1 Solutions

This post is created to help all the CBSE Class 8 students for the Solutions of Frank Learning Maths Class 8 Mathematics Book, Chapter 3 Squares and Square Roots Exercise 3.1. Here students can easily find step by step solutions of all the problems for Squares and Square Roots Exercise 3.1. Step by Step proper solutions for every problems. All the problem are solved with easily understandable methods with proper guidance so that all the students can understand easily.

Chapter 3 – Squares and Square Roots

Squares and Square Roots – Exercise 3.1 all Questions Solution

(1) Find the Square of the following by multiplication

Solution :

(a) 192

= 19 × 19

= 361

(b) 472

= 47 × 47

= 2209

(c) 622

= 62 × 62

= 3844

(d) 1012

= 10201

(2) Find the Pythagorean triplets of the numbers, the smallest of which is given below

Solution :

Let, Pythagorean triplets are 2m, m2 – 1, m2 + 1

(a) 2 m = 6

M = 3

M2 – 1 = 9 – 1 = 8

M2 + 1 = 9 + 1 = 10

(b) 2 m = 14

M = 7

M2 = 1 = 48

M2 + 1 = 50

(c) 2m = 18

M = 9

= M2 + 1 = 82

(d) 2 m = 16

M = 8

M2 – 1 = 63

M2 + 1 = 65

(3) Evaluate the following using properties of perfect squares

Solution :

(a) (29)2 – (28)2

=(29 + 28) (29 – 28)

= 57

(b) (68)2 – (67)2

= (68 – 67) (68 +67)

= 135

(c) (121)2 – (120)2

= (121) (121 – 120) (121 + 120)2

= 241

(d) (278)2 – (277)2

= (278 – 277) (278 + 277)

= 555

Question no – (4)

Solution :

LCM of 8, 9, 10 = 360

360 = 2 × 2 × 2 × 3 × 3 × 3 × 5

We should multiple the given number with (2 × 5) for perfect square.

360 × 10 = 36000

Therefore, 3600 is the perfect square.

Question no – (5)

Solution :

∴ LCM = 180

= 2 × 2 × 3 × 3 × 5

∴ We should multiple the number by 5

∴ 180 × 5 = 900

Thus, the least square number is 900

Question no – (8)

Solution :

(i) 92 – 82

= 81 – 64

= 17

(ii) 132 – 122

= 25

Therefore, the Natural numbers between then 16 and 24

Question no – (9)

Solution :

(a) 502 – 512

= (51 + 50) (51 – 50)

= 101
∴ Non-squares number between 512, 502 = (101 – 1)

= 100

(b) 902 – 912

= (91 + 90) (91 – 90)

= 181

∴ Non-square number (181 – 1) = 180

(c) 10002 – 10012

= (1001 + 1000) ( 1001 – 1000)

= 2001

∴ Non-square numbers (2001 – 1) = 2000

Question no – (10)

Solution :

(a) 13 × 15

= 13 (13 + 2)

= 132 + 13 x 2

= 169 + 26

= 195

(b) 28 × 30

= (30 – 2) x 30

= 302 – 2 x 30

= 900 – 60

= 840

(c) 53 × 55

= (55 – 2) x 55

= (55)2 – 2 x 55

= 3025 – 120

= 2905

(d) 100 × 102

= 100 (100 + 2)

= 1002 + 2 x 100

= 10000 + 200

= 10200

Updated: February 2, 2023 — 3:31 pm