AP Board 8th Class Maths Solutions Chapter 6 Square Roots and Cube Roots Ex 6.1

AP State Syllabus AP Board 8th Class Maths Solutions Chapter 6 Square Roots and Cube Roots Ex 6.1 Textbook Questions and Answers.

AP State Syllabus 8th Class Maths Solutions 6th Lesson Square Roots and Cube Roots Exercise 6.1

Question 1.
What will be the units digit of the square of the following numbers?
(i) 39
(ii) 297
(iii) 5125
(iv) 7286
(v) 8742
Solution:

Number	Square of the units digIt	Units digit of a squared number
i) 39	9² = 9 x 9 = 81	1
ii) 297	7² = 7 x 7 = 49	9
Iii) 5125	5² = 5 x 5 = 25	5
iv) 7286	6² = 6 x 6 = 36	6
v) 8742	2² = 2 x 2 = 4	4

Question 2.
Which of the following numbers are perfect squares?
(i) 121
(ii) 136
(iii) 256
(iv) 321
(v) 600
Solution:

Number	Prime factorizatlon	Perfect square numbers Yes/No
i) 121	121 = 11 x 11 = 11²	yes
ii) 136	136 = 8 x 17 = 2 x 2 x 2 x 17	No
iii) 256	256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 2⁸= (2⁴)²	yes
iv) 321	321 = 3 x 107	No
v) 600	600 = 120 x 5 = 12 x 10 x 5 = 2 x 2 x 2 x 3 x 5 x 5	No

Question 3.
The following numbers are not perfect squares. Give reasons?
(i) 257
(ii) 4592
(iii) 2433
(iv) 5050
(v) 6098
Solution:
i) 257 → The units digit of the number is 7. So it is not a perfect square number.
ii) 4592 → The units digit of the number is 2. So it is not a perfect square number.
iii) 2433 → The units digit of the number is 3. So, it is not a perfect square number.
Iv) 5050 → The last two digits of the number are not two zero’s. So, it is not a perfect square number.
v) 6098 → The units digit of the number is 8. So It is not a perfect square number

Question 4.
Find whether the square of the following numbers are even or odd?
(i) 431
(ii) 2826
(iii) 8204
(iv) 17779
(v) 99998
Solution:

Number	Units digit of square of a number	Even / Odd
(i) 431	1² = 1	1 , odd
(ii) 2826	6²= 36	6, odd
(iii) 8204	4² = 16	6 , even
(iv)17779	9²= 81	1 , odd
(v) 99998	8²= 64	4 , even

Question 5.
How many numbers lie between the square of the following numbers
(i) 25; 26
(ii) 56; 57
(iii) 107;108
Solution:
The numbers lie between the square of the numbers are:
1) 25,26 → 2 x 25=50
ii) 56, 57 → 2 x 56 = 112
iii) 107, 108 → 2 x 107 = 214

Question 6.
Without adding, find the sum of the following numbers
(i) 1 + 3 + 5 + 7 + 9 =
(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 =
(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 =
Solution:
(i) 1 + 3 + 5 + 7 + 9 = (5)² = 5 x 5 = 25
[∵ Sum of ‘n’ consecutive odd number = n²]
(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 9² = 9 x 9 = 81
(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 = 13² = 13 x 13 = 169