Question

Find the square root of $144$ by the method of repeated subtraction.

Answer 1

As explained in Properties of Square Numbers the square number is the sum of successive odd numbers starting from 1 and you can find the square root of a number by repeatedly subtracting successive odd numbers( which is also starting from 1) from the given square number, till you get zero.

$1.44-1=143$

$2.143-3=140$,

$3.140-5=135$

$4.135-7=128,$

$5.128-9=119,$

$6.119-11=108,$

$7.108-13=95,$

$8.95-15=80,$

$9.80-17=63,$

$10.63-19=44,$

$11.44-21=23,$

$12.23-23=0$

$\therefore \sqrt{144}=12$.