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Squares and square roots

Palak K.
28/05/2019 0 0

 Q 1).Express 49 as a sum of 7 odd numbers

  1. To solve this we first see 49=7^2

So if we add 1+3+5+7+9+11+13, we get 49

Q.2)Express 121 as a sum of 11 odd numbers

  1. We see 121=11^2, So if we add first 11 odd numbers starting from 11 we get 121.

So 1+3+5+7+9+11+13+15+17+19+21,we get 121

Without adding, find the sum.

(i) 1 + 3 + 5 + 7 + 9

(ii) 1 + 3 + 5 + 7 + 9 + I1 + 13 + 15 + 17 +19

(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

The general pattern is when we add consecutive odd numbers starting from 1,the sum is square of number of odd numbers.

So (i) sum is 5^2=25

(ii)Here consecutive odd numbers=10, so sum is 10^2=100

(iii) Here consecutive odd numbers=12,so sum is 12^2=144

 

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