Page 58 - Start Up Mathematics_8 (Non CCE)

Here n = 7
2
2
2
\ 15 = (2 × 7 + 2 × 7) + (2 × 7 + 2 × 7 + 1)
= (2 × 49 + 2 × 7) + (2 × 49 + 2 × 7 + 1)
= (98 + 14) + (98 + 14 + 1) = 112 + 113
Example 9: Observe the following pattern:
2
2
2
11 × (sum of digits of 11 ) = 11 × (1 + 2 + 1) = 22 2
2
2
2
111 × (sum of digits of 111 ) = 111 × (1 + 2 + 3 + 2 + 1) = 333 2
2
2
2
1111 × (sum of digits of 1111 ) = 1111 × (1 + 2 + 3 + 4 + 3 + 2 + 1) = 4444 2
2
2
Now find the value of: 111111 × (sum of digits of 111111 )
2
Solution: (111111) = 12345654321
2
Sum of digits of (111111) = 1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1
2
2
111111 × (sum of digits of 111111 )
2
= 111111 × (1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1) = 666666 2
Example 10: Observe the following pattern:
2
11 = 121
2
101 = 10201
2
1001 = 1002001
2
10001 = 100020001
2
Using this pattern, write the value of 10000001 .
2
Solution: According to the above pattern 10000001 should have 6 zeros between 2 and 1.
2
\ 10000001 = 100000020000001
EXERCISE 3.2
1. Which of the following numbers are not perfect squares? Give reasons.
(a) 7,921 (b) 12,288 (c) 4,205 (d) 2,209 (e) 7,442
2. The squares of which of the following numbers will be odd numbers?
(a) 131 (b) 2,136 (c) 4,259 (d) 628 (e) 104
3. What will be the units digit of the squares of the following numbers?
(a) 62 (b) 6,555 (c) 277 (d) 7,431 (e) 18,324
4. Observe the following pattern and write the value of 1 + 3 + 5 + 7 + 9 + 11 + ... + 27.
1 + 3 = 4 = 2 2
1 + 3 + 5 = 9 = 3 2
1 + 3 + 5 + 7 = 16 = 4 2
1 + 3 + 5 + 7 + 9 = 25 = 5 2 4444 2 7777777 2
5. Using a suitable pattern find the value of: (a) (b)
1234321 1234567654321
2
6. Observe the following pattern and find the value of 10101010101 .
2
11 = 121
2
101 = 10201
2
10101 = 102030201
2
1010101 = 1020304030201

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