Class 08 Activity – Dividing Square roots

Objective:

 Dividing square roots.

Procedure: 

Let the children note the following geometrical patterns. and deduce       

                                        1 = 1²

    1 + 3 = 2²

1 + 3 + 5 = 3²

     1 + 3 + 5 + 7 = 4²

1 + 3 + 5 + 7 + 9 = 5²

  1 + 3 + 5 + 7 + 9 + 11 = 6²

     1 + 3 + 5 + 7 + 9 + 11 + 13 = 7²

This geometrical pattern verifies that the sum of the first n odd numbers is n²? 

Conversely, any square number can be decomposed into the sum of a number of odd natural numbers. If a given number can be expressed as the sum of first n natural odd numbers, then the number must be the square of the number n, which will accordingly be the square root of the given number. This fact can be used to find the square root of small numbers. 

To find the square root of any number, we subtract from it consecutively 1,3,5,7,9,11, …..

The number times we have to subtract to get 0, gives the square root of the given number. 

Here the procedure is shown for 81 and 110. 

From 81, we have to subtract the first 9 odd natural numbers, to get 0.Therefore, square root of 81 is 9. 

From 110, we have to subtract first 10 odd natural numbers and we cannot subtract the first 11 odd natural numbers. 

Thus, 110 is not a square number and its square root lies between 10 and 11.