# 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.