Every natural number squared can be written as the sum of consecutive odd natural numbers starting from zero.
Find the square root of 121 by repeated subtraction method.
We will use this fact to find the square root of a number by repeated subtraction.
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To find the square root of sqrt 121 by repeated subtraction we will subtract successive odd numbers starting from 1 from 121.
Therefore 4 is the square root of 16.
To find square root we subtract consecutive odd numbers from number till we obtain 0 square root total numbers subtracted let s take an examplesuppose we need to find 81square root of 8181 1 8080 3 7777 5 7272 7 6565 9 5656 11 4545 13 3232 15 1717 17 0since aft.
100 1 99 99 3 96 96 5 91 91 7 84 84 9 75 75 11 64 64 13 51 51 15 36 36 17 19 19 19 0 to find the square root we subtract successive odd numbers from the number till we obtain 0.
Ex 6 3 3 find the square roots of 100 and 169 by the method of repeated subtraction.
Let us study how to find the square root of 121 by repeated subtraction method.
Say you are required to find the square root of 121 that is 121.
Let us take an example to learn this method.
15 3 12 step 3.
Square root of 121 by repeated subtraction.
Example 1 find the square root of 144 by the subtraction method.
7 7 0 as you can see that given number 16 was repeatedly subtracted by successive odd numbers starting from 1 and we get zero in forth step.
Square root of 100.
The number of steps to reach zero is the square root.
Find square root of 16 by repeated subtraction method.
12 5 7 step 4.
So for finding square root we start subtraction from 1 and continue until it reaches zero.
