Question

the square root of 144 and 225 by the method of repeated subtraction ​

Answer 1

Answer:

12 ,15

Step-by-step explanation:

12*12=144

15*15=225

Answer 2

As explained in Property 4 of Square Numbers  and the square number is the sum of successive odd numbers starting from 1 and you can find 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.  

44-1=143, 143-3=140, 140-5=135, 135-7=128, 128-9=119, 119-11=108, 108-13=95, 95-15=80, 80-17=63, 63-19=44, 44-21=23, 23-23=0, √144=12.

225-1=224, 224-3=221, 221-5=216, 216-7=209, 209-9=200, 200-11=189, 189-13=176, 176-15=161, 161-17=144, 144-19=125, 125-21=104, 104-23=81, 81-25=56, 56-27=29, 29-29=0

So square root of 225=15