GSEB Solutions Class 8 Maths Chapter 6 Square and Square Roots Ex 6.1

Gujarat Board GSEB Textbook Solutions Class 8 Maths Chapter 6 Square and Square Roots Ex 6.1 Textbook Questions and Answers.

Gujarat Board Textbook Solutions Class 8 Maths Chapter 6 Square and Square Roots Ex 6.1

Question 1.
What will be the unit digit of the squares of the following numbers?

1. 81
2. 272
3. 799
4. 3853
5. 1234
6. 26387
7. 52698
8. 99880
9. 12796
10. 55555

Solution:
1. ∵ 1 × 1 = 1
∴ The unit digit of (81)² will be 1.

2. ∵ 2 × 2 = 4
The unit digits of (272)² will be 4.

3. Since, 9 × 9 = 81
∴ The unit digit of (799)² will be 1.

4. Since, 3 × 3 = 9
∴ The unit digit of (3853)² will be 9.

5. Since, 4 × 4 = 16
∴ The unit digit of (1234)² will be 6.

6. Since 7 × 7 = 49
∴ The unit digit of (26387)² will be 9.

7. Since, 8 × 8 = 64
∴ The unit digit of (52698)² will be 4.

8. Since 0 × 0 = 0
∴ The unit digit of (99880)² will be 0.

9. Since 6 × 6 = 36
∴ The unit digit of (127969)² will be 6.

10. Since, 5 × 5 = 25
∴ The unit digit of (555559)² will be 5.

Question 2.
The fòllowing numbers are obviously not perfect squares. Give reason?

1. 1057
2. 23453
3. 7928
4. 222222
5. 64000
6. 89722
7. 222000
8. 505050

Solution:
1. 1057
Since, the ending digit is 7 (which is not one of 0, 1, 4, 5, 6 or 9)
∴ 1057 is not a perfect square.

2. 23453
Since, the ending digit is 7 (which is not one of 0, 1, 4, 5, 6 or 9).
∴ 23453 is not a perfect square.

3. 7928
Since, the ending digit is 8 (which is not one of 0, 1, 4, 5, 6 or 9).
∴ 7928 is not a perfect square.

4. 222222
Since, the ending digit is 2 (which is not one of 0, 1, 4, 5, 6 or 9).
∴ 222222 is not a perfect square.

5. 64000
Since, the number of zeros is odd.
∴ 64000 is not a perfect square.

6. 89722
Since, the ending digits is 2 (which is not one of 0, 1, 4, 5, 6 or 9).
∴ 89722 is not a perfect square.

7. 222000
Since, the number of zeros is odd.
∴ 222000 is not a perfect square.

8. 505050
The units digit is odd zero.
∴ 505050 can not be a perfect square.

Question 3.
The squares of which of the following would be odd numbers?

1. 431
2. 2826
3. 7779
4. 82004

Solution:
Since the square of an odd natural number is odd and that of an even number is an even number.
1. ∴ The square of 431 is an odd number.
[∵431 is an odd number]

2. The square of 2826 is an even number.
[∵ 2826 is an even number]

3. The square of 7779 is an odd number.
[∵ 7779 is an odd number]

4. The square of 82004 is an even number.
[∵ 82004 is an even number]

Question 4.
Observe the following pattern and find the missing digits?
11² = 121
101² = 10201
10101² = 1002001
1010101² = I …………….. 2 …………………. 1
10000001² = …………………………
Solution:
Observing the above pattern, we have

• (100001)² = 10000200001
• (10000001)² = 100000020000001

Question 5.
Observe the following pattern and supply the missing number?
11² = 121
101² = 10201
10101² = 102030201
1010101² = ………………………..
…………………… ² = 10203040504030201
Solution:
Observing the above, we have

• (1010101)² = 1020304030201
• 10203040504030201 = (101010101)²

Question 6.
Using the given pattern, find the missing numbers?
1² + 2² + 3² = 3²
2² + 3² + 6² = 7²
3² + 4² + 12² = 13²
4² + 5² + _² = 21²
5² + _² + 30² = 31²
6² + 7² + _² = _²
Note:
To find pattern:
Third number is related to first and second number. How?
Fourth number is related to third number. How?
Soution:
The missing numbers are

1. 4² + 5² + 20² = 21²
2. 5² + 6² + 30² = 31²
3. 6² + 7² + 42² = 43²

Question 7.
Without adding, find the sum,

1. 1 + 3 + 5 + 7 + 9
2. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 13 + 17
3. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

Solution:

1. The sum of first 5 odd numbers = 5² = 25
2. The sum of first 10 odd numbers = 10² = 100
3. The sum of first 12 odd numbers = 12² = 144

Question 8.

1. Express 49 as she suns of 7 odd numbers.
2. Express 121 as the suns oft! odd numbers.

Solution:
1. 49 = 7² Sum of first 7 odd numbers
= 1 + 3 + 5 + 7 + 9 + 11 + 13

2. 121 = 11² = Sum of first 11 odd numbers
= 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21

Question 9.
How mars numbers lie between squares of the following numbers?

1. 12 and 13
2. 25 and 26
3. 99 and 100

Solution:
Since between n² and (n + 1)², there are 2n, non-square numbers.

1. Between 12² and 13², there are 2 × 12, ie; 24 numbers
2. Between 25² and 26², there are 2 × 25, i.e; 50 numbers
3. Between 99² and 100², there arc 2 × 99. i.e; 198 numbers