Question

"Question 8 (i) Express 49 as the sum of 7 odd numbers. (ii) Express 121 as the sum of 11 odd numbers.

Class 8 Squares and Square Roots Page 96"

Answer 1

The square of a natural number can be expressed as a sum of n odd numbers.

Conversely we can say that the sum of the first n odd  numbers is equal to the square of n(n²).

1 + 3 = 2² = 4
1 + 3 + 5 = 3² = 9
1 + 3 + 5 + 7 = 4² =16
1 + 3 + 5 + 7 + 9 = 5² = 25

So Sum of n odd numbers starting from 1 = n²

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Solution:

1) Since, 49 = 7²

49 can be written as :

1 + 3 + 5 + 7 + 9 + 11 + 13= 7²= 49

2) Since, 121 = 11²

121 can be written as:

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 = 11²= 121

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Hope this will help you....

Answer 2

(i) 49 is the square of 7. Therefore it is the sum of 7 odd numbers. 49 = 1 + 3 + 5 + 7 + 9 + 11 + 13

(ii) 121 is the square of 11. Therefore it is the sum of 11 odd numbers 121 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21