Squares And Square Roots
Exercise 5.2
1). Find the square of the following numbers.
(i) 32 (ii) 35
(iii) 86 (iv) 93
(v) 71 (vi) 46
Solution:
(i) 32
32 = 30 + 2
(a+b)2 = a2 + 2ab + b2
322 = (30 + 2)2
= (30)2 + 2 X 30 X 2 + (2)2
= 900 + 120 + 4
= 1024
(ii) 35
35 = 30 + 5
(a+b)2 = a2 + 2ab + b2
352 = (30 + 5)2
= (30)2 + 2 X 30 X 5 + (5)2
= 900 + 300 + 25
= 1225
(iii) 86
86 = 80 + 6
(a+b)2 = a2 + 2ab + b2
862 = (80 + 6)2
= (80)2 + 2 X 80 X 6 + (6)2
= 6400 + 960 + 36
= 7396
(iv) 93
93 = 90 + 3
(a+b)2 = a2 + 2ab + b2
932 = (90 + 3)2
= (90)2 + 2 X 90 X 3 + (3)2
= 8100 + 540 + 9
= 8649
(v) 71
71 = 70 + 1
(a+b)2 = a2 + 2ab + b2
712 = (70 + 1)2
= (70)2 + 2 X 70 X 1 + (1)2
= 4900 + 140 + 1
= 5041
(vi) 46
46 = 40 + 6
(a+b)2 = a2 + 2ab + b2
462 = (40 + 6)2
= (40)2 + 2 X 40 X 6 + (6)2
= 1600 + 480 + 36
= 2116
2). Write a Pythagorean triplet whose one member is.
(i) 6 (ii) 14
(iii) 16 (iv) 18
Solution:
(i) 6
We can get Pythagorean triplets by using general form 2m, m2 – 1,
m2 + 1.
Let m2 – 1 = 6
m2 = 6 + 1
m2 = 7
m cannot be an integer.
Let m2 + 1 = 6
m2 = 6 – 1
m2 = 5
m cannot be an integer
therefore, let 2m = 6
m = 3
m2 – 1 = 32 – 1 = 9 – 1 = 8
m2 + 1 = 32 + 1 = 9 + 1 = 10
Ans: The Pythagorean triplets are 6, 8, 10.
(ii) 14
We can get Pythagorean triplets by using general form 2m, m2 – 1,
m2 + 1.
Let m2 – 1 = 14
m2 = 14 + 1
m2 = 15
m cannot be an integer.
Let m2 + 1 = 14
m2 = 14 – 1
m2 = 13
m cannot be an integer
therefore, let 2m = 14
m = 7
m2 – 1 = 72 – 1 = 49 – 1 = 48
m2 + 1 = 72 + 1 = 49 + 1 = 50
Ans: the Pythagorean triplets are 14, 48, 50.
(iii) 16
We can get Pythagorean triplets by using general form 2m, m2 – 1,
m2 + 1.
let 2m = 16
m = 8
m2 – 1 = 82 – 1 = 64 – 1 = 63
m2 + 1 = 82 + 1 = 64 + 1 = 65
Ans: the Pythagorean triplets are 16, 63, 65.
(iv) 18
We can get Pythagorean triplets by using general form 2m, m2 – 1,
m2 + 1.
let 2m = 18
m = 9
m2 – 1 = 92 – 1 = 81 – 1 = 80
m2 + 1 = 92 + 1 = 81 + 1 = 82
Ans: the Pythagorean triplets are 18, 80, 82
Click here for the solutions of Std 8 Maths
1). Rational Numbers
2). Linear Equations in One Variable
3). Understanding Quadrilaterals
4). Data Handling
5). Squares and Square Roots
