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8.(i) Express 49 as the sum of 7 odd numbers.
(ii) Express 121 as the sum of 11 odd numbers.
9. How many numbers lie between squares of the following numbers?
(i) 12 and 13
(ii) 25 and 26
(iii) 99 and 100
"
8. (i) Given: Express 49 as the sum of 7 odd numbers.
To find: We have to express 49 as the sum of 7 odd numbers
Solution:
1 + 3 + 5 + 7 + 9 + 11 + 13 = 49
8. (ii)
Given: Express 121 as the sum of 11 odd numbers.
To find: We have to express 121 as the sum of 11 odd numbers
Solution:1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 = 121
9.(i)
Given: 12 and 13.
To find: We have to find how many numbers lie between squares of 12 and 13.
Solution:
122 = 144
132 = 169
Now,
169 - 144 = 25
So, the number between squares of 12 and 13 is 25 - 1 = 24
9. (ii)
Given: 25 and 26
To find: We have to find how many numbers lie between squares of 25 and 26.
Solution:
252 = 625
262 = 676
Now,
676 - 625 = 51
So, number between squares of 25 and 26 is 51 - 1 = 50
9. (iii)
Given: 99 and 100.
To find: We have to find how many numbers lie between squares of 99 and 100.
Solution: 99 and 100
992 = 9801
1002 = 10000
Now,
10000 - 9801 = 199
So, number between squares of 99 and 100 is 199 - 1 = 198.